׉?4ׁB!בCט{u׉׉ 7cassandra://uZa5a110BWqb0s4ajrPGican1672PebyRIaHtP_3JHQX` ׉ 7cassandra://XP7cu97J0JR1suinzv2e7On95xrOUyWwPuroysw7G-MYB`S׉ 7cassandra://rS63f6I2cr5dj3a4bZRcZqRF6UcBStcO4vKbjQ1y5ZU"`̵׉ 7cassandra://Y_z9y7qVzvZ8J2L8hn9Av1qK0znMVv4U2u7GFls2S2Uš̆͠[ )Cט{u׈׈E[ )C׉E;Koninklijk Actuarieel Genootschap PROJECTION TABLE AG 2016 ׉ 7cassandra://rS63f6I2cr5dj3a4bZRcZqRF6UcBStcO4vKbjQ1y5ZU"`̵[ )C[ )C{בCט{u׉׉ 7cassandra://fXRbSx7JhxFIOEtMBpl0mqoo1GLEIGJE8lsZ_zkyPX4;K` ׉ 7cassandra://RiOuDqjFjZ0H8PAs1ZVfhq7Gt6xCkCR2ypRx5Bu-w-YG`S׉ 7cassandra://Hc99N7OJ9Th8HY-4ZS7SzrsxjHJjwVvphqb9X8GGuE4`̵׉ 7cassandra://hEi0MddS8IZaGD0NCjH0RS_7f1MwHypGaobVv4m3voE͢ :͠[ )Cט{u׉׉ 7cassandra://usZt2y8TJ_8wDxoH2TFAfT2RSEqfFTfcbJbiyLm4kw8&` ׉ 7cassandra://UEKF2Kdv1FW79trERLC7JGWlh1i8xTaE5-JVkLbcp-cG`׉ 7cassandra://DIHymsuFLSVuABwMpdHEqwXabgPfBtplupCGcVT7wpM&`j׉ 7cassandra://8pA-Ly1-QlhacRvS1Cn9_UwuRAGpzR0B-w09ocpR-LI..͠ [ )C׉EDPROJECTION TABLE AG2016 13 September 2016 1 Projection Table AG2016 ׉ 7cassandra://Hc99N7OJ9Th8HY-4ZS7SzrsxjHJjwVvphqb9X8GGuE4`̵[ )C׉E *1 FOREWORD Life expectancy in the Netherlands has increased steadily during the past 50 years. This trend has had a considerable impact on society. For pension funds and life insurers it is important to have continuous insight into this development in order to be able to fulfil the promises they have made. The Royal Dutch Actuarial Association (Koninklijk Actuarieel Genootschap or ‘AG’) sees it as its role to provide the financial sector with an insight into these developments by means of projection life table. The new Projection Table AG2016 is based on the same model which formed the basis for Projection Table AG2014. It is a fully transparent model with a limited number of parameters, so that it can be explained well and can be reconstructed precisely. This is consistent with the Association’s aim of making knowledge accessible to and applicable by the financial sector. The most important characteristic of the projections in AG2016 is stated below: Projection Table AG2016 is based on a stochastic model, as a result of which it is also possible for pension funds and life insurers to estimate the uncertainty of the projections. This is important in setting the prices of financial derivatives and determining the buffers to be maintained in relation to uncertainties regarding mortality. In addition to historic mortality in the Netherlands, Projection Table AG2016 is also based on the mortality of a number of European countries with a comparable level of prosperity. This combination of data results in a stable model which is less sensitive to incidental variances in a particular year in the Netherlands. On the basis of Projection Table AG2016, it is possible to estimate mortality in the distant future. It is possible to monitor someone born in 2016 throughout his or her life because mortality can be estimated for every future age. Projection Table AG2014 was determined separately for men and women. In the case of the projection life table for 2016, use was made of the correlation between the development of mortality amongst men and women. In this publication, the Association’s Mortality Research Committee discusses the development and outcomes of Projection Table AG2016 in more detail. As the chairman of the Royal Dutch Actuarial Association, I wish to express my gratitude to the members of the Mortality Research Committee and the members of the Projection Tables Working Group for the considerable good work that they have done. On behalf of the Board of the Royal Dutch Actuarial Association. Jan Kars AAG Chairman 2 Projection Table AG2016 Foreword 3 ׉ 7cassandra://DIHymsuFLSVuABwMpdHEqwXabgPfBtplupCGcVT7wpM&`j[ )C[ )C {בCט{u׉׉ 7cassandra://X4SWIq8X6-UzUQ7t5p1uUKDyw_zSGVfzAybhj6lC3xQ^` ׉ 7cassandra://lBZNHphOTRK-82yoZ-AhG38_n4PmgLIofbG7wLHw-BcLC`׉ 7cassandra://Wv1BP49S4hmQtHnr4CY906YdPxEs9z65nGvHAaMf9oEN`j׉ 7cassandra://ofoX3WQlv1LVFDkIBvAE7f1OyVWC64jDvWHTBkaF-DI8.͠ [ )C׉EProjection Table AG2016 4 ׉ 7cassandra://Wv1BP49S4hmQtHnr4CY906YdPxEs9z65nGvHAaMf9oEN`j[ )C׉E 2 JUSTIFICATION Mortality Research Committee Monitoring the development of mortality in the Netherlands and developing projections of this has traditionally been an important task of the Royal Dutch Actuarial Association. This is expressed in the long series of period mortality and life tables which the Association has published. In 2011, the Board of the Association set up the Mortality Research Committee and assigned it the task of publishing a new projection life table every two years, which was to serve as the basis for estimating the future life expectancy of the population of the Netherlands. In 2014, a model was implemented which, in addition to the mortality projection, also reflects the uncertainty in this model (a so-called stochastic model). This resulted in the publication of AG2014. During the past two years, the Mortality Research Committee has drawn up Projection Table AG2016. This projection life table is based on the same model as AG2014, with a number of changes to the data used and the method of estimation. In particular, AG2016 offers an insight into the correlation between the development of mortality amongst men and women. By doing so, the Committee has taken the requests from the sector into account. A full overview of the changes in AG2016 relative to AG2014 can be found in chapter 6. The committee consists of members with an academic background, members from the pension and insurance sector with a technical background and members from these sectors with a policy background. The Mortality Research Committee consisted of the following members in mid-2016: B.L. de Boer AAG, Chairperson drs. W. de Boer AAG drs. C.A.M. van Iersel AAG CERA, Secretary drs. J. de Mik AAG dr. H.J. Plat AAG RBA dr. ir. T.J.W. Schulteis AAG prof. dr. ir. M.H. Vellekoop prof. dr. B.J.M. Werker ir. drs. M.R. van der Winden AAG MBA Projection Tables Working Group The Mortality Research Committee set up the Association’s Projection Tables Working Group at the end of 2012 with the task of supporting the Committee in the development of projection life tables. The Projection Tables Working Group consisted of the following members in mid-2016: H.K. Kan MSc AAG C.C. Loois MSc W.G. Ouburg MSc AAG FRM, Chairperson drs. E.J. Slagter FRM ir. drs. J.H. Tornij M.A. van Wijk MSc AAG 1 – Projection Table AG2014 of 9 September 2014 Projection Table AG2016 Within the framework of its task, the Working Group carried out various analyses in order to arrive at the AG2016 projection. On the basis of these analyses, the Mortality Research Committee made a number of choices which are explained in this publication. The definitive model was adopted on the basis of the choices made by the Mortality Research Committee. This model has been implemented and documented by the Working Group. Justification 5 [ )C[ )C{בCט{u׉׉ 7cassandra://2tbAUxFGuctf-FEQMpQc1-PB4NMW6HMEFHdrXEEh5_sx` ׉ 7cassandra://GsSujJC7ffRDol3GrYOXKg1zeQIIKQuXsPV1sjFwbh0B`׉ 7cassandra://StDL59TeyPQq5sBFHr1uyiHRyJj3RfE4Y5YsysC5y5Qm`j׉ 7cassandra://O6ZHaJlzbgF8ekNEJqd3nTArTs37-fI8yr-Y2OpvdE09.͠ [ )C׉EProjection Table AG2016 6 ׉ 7cassandra://StDL59TeyPQq5sBFHr1uyiHRyJj3RfE4Y5YsysC5y5Qm`j[ )C׉EX3 CONTENTS 1 Foreword –3 2 Justification –5 3 Contents –7 4 Summary –9 5 Introduction –10 5.1 Biennial update of the estimate of mortality probabilities – 10 5.2 Developments in the method – 10 5.3 Definition of life expectancy – 10 5.4 Retirement age of the state old-age benefit (AOW) and the standard retirement age – 11 5.5 Structure of the report – 11 5.6 Publication of the projection tables on the Association’s website – 11 6 Mortality data and assumptions of the model –12 6.1 Mortality data – 12 6.2 Assumptions of the model – 14 6.3 Summary of the changes in the Projection Table AG2016 relative to AG2014 – 16 7 Uncertainty –17 7.1 Extrapolation from the past – 17 7.2 No parameter and model uncertainty – 17 7.3 Distinction between uncertainty in mortality probabilities and uncertainty in mortality figures – 18 8 Outcomes –19 8.1 Observations in relation to AG2014 – 19 8.2 From AG2014 to AG2016 – 20 8.3 Future life expectancy – 21 8.4 Projection in perspective – 21 8.5 Link between life expectancy at the age of 65 and the retirement age in the first and second tiers – 23 8.6 Effects on the provisions – 24 9 Applications of the model –26 9.1 Simulating the value of the liabilities – 27 9.2 Simulating the best-estimate value in a year’s time – 29 9.3 Simulating life expectancy – 29 10 Appendices –31 Appendix A – Projection Model AG2016 - Technical description – 32 Appendix B – Model portfolio – 40 Appendix C – Literature and data used – 42 Appendix D – Glossary – 43 Colophon –46 Projection Table AG2016 Contents 7 [ )C[ )C{בCט{u׉׉ 7cassandra://vWR0up66Y4e-6wBkjxK229ss6NvG9d99-eS1d0RgtJQ` ׉ 7cassandra://AlRFrkO2zelTOaSlZBzJiTr2Dhlv0DFEEaOBTsvKIjg@J`׉ 7cassandra://iPWzmcW_AH_3bqtIQC3jYUqjHMo79ikMIKuCeF0xlNMj`j׉ 7cassandra://yG3cRvkqcyPm3bkWYlU6N_tdTQwGxbOAFMa5DOeSn5E,P.͠ [ )C׉EProjection Table AG2016 8 ׉ 7cassandra://iPWzmcW_AH_3bqtIQC3jYUqjHMo79ikMIKuCeF0xlNMj`j[ )C׉E4 SUMMARY With the publication of the Projection Table AG2016, the Actuarial Association presented its most recent estimate of the future mortality of the population of the Netherlands. This estimate is based on both mortality data pertaining to the Netherlands and data pertaining to European countries that have a level of prosperity comparable to that of the Netherlands. The Projection Table AG2016 is based on a stochastic model. In comparison to the Projection Table AG2014, an estimate is also given of the correlation between the development of the mortality of men and women. The Projection Table AG2016 replaces Projection Table AG2014. From the most recent data it appears that mortality for both men and women is still falling and that life expectancy is continuing to rise. On the basis of the most recent insights, the life expectancy of a girl born in 2016 is 93.0 years and that of a boy born in 2016 90.1 years. These life expectancies have been calculated on the basis of the socalled cohort life expectancy and take into account all the expected future developments in mortality. The life expectancy of boys and girls born in 50 years’ time is expected to rise further by 3 to 4 years. Pension funds and insurance companies may use the Projection Table AG2016 to determine and assess their technical provisions and premiums. The effects will not be the same for all portfolios. Their composition in terms of age and sex, in particular, will determine the effects on a specific portfolio. In general, it may be concluded that in the case of an actuarial discount rate of 3% in relation to portfolios with relatively many men, the technical provisions will increase slightly (0.2%) and in relation to portfolios with relatively many women the technical provisions will increase more (0.5%). At the aggregate level, the Projection Table AG2016 is more onerous than the Projection Table AG2014 in relation to technical provisions. If the Projection Table AG2016 were to be used to determine the State Pension age (AOW) on the next occasion that it is determined (2017), on the basis of present legislation the State Pension age in 2022 is expected to increase further to 67 years and three months. Projection Table AG2016 Summary 9 [ )C[ )C{בCט{u׉׉ 7cassandra://E6k6ZI7GGr2beoD9Aw_UlPSRLAavcnQU3MMSaVtCYJs` ׉ 7cassandra://ALPc_sKwwnpQPAdZNNdfYIrT3veouNKIYeui_7OrBSAo|`׉ 7cassandra://KMGKCvUih_D_nKsP-fgWluMgyt-Uk8DYfSuc9-zcvME x`j׉ 7cassandra://ykbN3ccHezqw72PRJrtocuL0SLSmwlLVftohb7rCHQkC2͠ [ )Cנ[ )CC9ׁH5http://www.ag-ai.nl/ActuarieelGenootschap/Publicatiesׁ ׁ Ј׉E 5 INTRODUCTION In this publication, an estimate is presented of the development of mortality probabilities and life expectancy in the Netherlands. This estimate is based on the most recent mortality data for the Netherlands and European countries with a comparable level of prosperity. 5.1 Biennial update of the estimate of mortality probabilities Every two years the Association publishes an update of the projection model with which projections can be made of the development of the mortality probabilities of the population of the Netherlands. This model is relevant to pension funds and life insurance companies because it can be used to estimate the level of technical provisions. Publicly available data from the Human Mortality Database (HMD), supplemented, where necessary, with data from Eurostat and data from Statistics Netherlands, form the basis for the new Projection Table AG2016. Data is available for the selected European countries up to and including 2014. In the case of the Netherlands, mortality observations are also available for 2015. 5.2 Developments in the method A stochastic model was introduced with the previous projections life table, Projection Table AG2014. This makes it possible to give an impression of the uncertainty in the development of life expectancy. The projection is also not limited to an horizon of 51 years, so that life expectancies can be calculated for cohorts. The Projection Table AG2016 also gives an estimate of the correlation between the development in the mortality of men and women. 5.3 Definition of life expectancy There are two definitions of life expectancy. A classic definition of life expectancy is so-called ‘period life expectancy’. This period life expectancy is based on the mortality probabilities in a particular period, for instance within a calendar year, and assumes that mortality probabilities in the future will remain the same. Period life expectancy therefore does not take into account future expected developments in mortality probabilities. This definition is often used to compare developments over time, but cannot be used to estimate how long people are still expected to live. The second definition, cohort life expectancy, on the other hand, does take into account future developments in mortality. Cohort life expectancy is based on the expected developments in mortality probabilities in future calendar years. Projection Table AG2016 Introduction 10 ׉ 7cassandra://KMGKCvUih_D_nKsP-fgWluMgyt-Uk8DYfSuc9-zcvME x`j[ )C׉ECohort life expectancy is therefore higher than period life expectancy, if mortality probabilities are expected to fall. Where the term ‘life expectancy’ is used in this publication, it should be assumed to mean ‘cohort life expectancy’. Where this document deviates from this, it has been explicitly stated which definition of life expectancy is intended. 5.4 Retirement age of the state old-age benefit (AOW) and the standard retirement age The State Pensions age (AOW) and the standard retirement age in the Netherlands are linked to the development of period life expectancy. The foreseen effects resulting from the Projection Table AG2016 are discussed in chapter 8 of this publication. 5.5 Structure of the report Chapter 6, ‘Mortality data and assumptions of the model’, deals with the considerations with regard to the model which played a role in drawing up Projection Table AG2016. What are the assumptions of the model? What data are used and what history is taken into account? In chapter 7, ‘Uncertainty’, an explanation is given of the the uncertainty that is taken into account in the model and that which is not. In chapter 8, ‘Outcomes’, the outcomes of the AG2016 projection are shown in terms of life expectancies and technical provisions. A comparison is also made with earlier projections. Finally, chapter 9, ‘Applications of the model’, contains a further explanation of the use of a stochastic model. 5.6 Publication of the projection life tables on the Association’s website The Association has published the projection life table and this publication, including the technical description of the projection model, on its website. See www.ag-ai.nl/ActuarieelGenootschap/Publicaties Projection Table AG2016 Introduction 11 [ )C[ )C{בCט{u׉׉ 7cassandra://jS3_053huZ1b1fWoPPTE73u8K4hqeVERb8WQA3bcXGU` ׉ 7cassandra://_QmY0CRuKZh2eDbMY9xatlVBT5IxIhPWrEt4m-oW7tEw`׉ 7cassandra://NiqnOCcMSW7sSBfSW8hE8WRj9LCySQlvJqoXK1ClEwE%`j׉ 7cassandra://aLJKFSh1vLiL9yDWYNz6iqK6E2jfknPQONXCiBnbqq0͛6*͠ [ )C׉E 6 MORTALITY DATA AND ASSUMPTIONS OF THE MODEL 6.1 Mortality data Mortality data for the Netherlands and Europe The point of departure for the present model is the stochastic model, introduced two years ago. This means that, in addition to mortality in the Netherlands, use was also made of data regarding the development of mortality in a number of other European countries. From 1970 onwards, the differences in mortality probabilities between a number of European countries have clearly decreased. In addition, a rising trend is observable in the development of life expectancy in these countries. In this regard, see graphs 1 and 2. For this reason, it was decided to base the projection for the Netherlands on the developments in comparable European countries. This ensures that the projection will not depend exclusively on data relating to the Netherlands, in which specific fluctuations may have occurred in the past, which do not necessarily say anything about future developments. The assumption is that the long-term increase in life expectancy in the Netherlands can be predicted more precisely by including a broader European population. The successive projections are also expected to be more stable than they would be if only data pertaining to the Netherlands were assumed. European mortality data The projection model makes use of European mortality data of countries whose Gross Domestic Product (GDP) lies above the European average. GDP is regarded as a measure of the wealth of a country. There is a positive correlation between prosperity and ageing: the higher the level of wealth, the older people become. The Netherlands is amongst the countries whose level of wealth is high and whose GDP is above the European average. On the basis of this criterion, the mortality data of the following European countries were included: Belgium, Denmark, Germany, Finland, France, Ireland, Iceland, Luxembourg, Norway, Austria, United Kingdom, Sweden and Switzerland. Where mention is made in the remainder of this publication to Europe or West Europe, these countries are meant. Relative to Projection Table AG2014, two amendments have been made to the data in addition to supplementing the data with recent data. Instead of only including England and Wales, it was decided to include the United Kingdom as a whole. The selection criterion is based on countries in Europe with an above-average GDP. The GDP for separate countries within the United Kingdom cannot be derived easily, but it is possible to derive GDP for the United Kingdom as a whole. This means extending the dataset to include Northern Ireland and Scotland, as part of the United Kingdom. In addition, it was decided to include the mortality figures of the former East Germany from 1990 onwards (because East Germany became part of Germany from that moment onwards). As a result of these changes, the dataset has been extended, while the average observed life expectancy in the dataset has fallen slightly. Projection Table AG2016 Mortality data and assumptions of the model 12 ׉ 7cassandra://NiqnOCcMSW7sSBfSW8hE8WRj9LCySQlvJqoXK1ClEwE%`j[ )C׉EPeriod life expectancy of men at birth 85 80 75 70 65 60 1950 1960 1970 1980 1990 2000 2010 Belgium France Netherlands Sweden Denmark Ireland Norway Switzerland Graph 1 Convergence of period life expectancy in a number of European countries, men at birth Period life expectancy of women at birth 90 Germany Iceland Austria Finland Luxembourg United Kingdom 85 80 75 70 65 1950 1960 1970 1980 1990 2000 2010 Belgium France Netherlands Sweden Denmark Ireland Norway Switzerland Graph 2 Convergence of period life expectancy in a number of European countries, women at birth Scope of the data Data for the observation period 1970 up to and including 2014 are used for the modelling. The most recent mortality rates from 2015 for the Netherlands are available and have therefore been added. There is no reason to change the starting point of the observation period. From 1970 onwards, there has been a stable development in the mortality rates (see also graphs 1 and 2). With the period chosen, historic data are used for a period of 45 years (from 1970 onwards). Projection Table AG2016 Mortality data and assumptions of the model 13 Germany Iceland Austria Finland Luxembourg United Kingdom [ )C[ )C{בCט{u׉׉ 7cassandra://ukvS1ZnLhGzXiVtteDNY5R2DGo_gOG6YvbO1HiwOt98` ׉ 7cassandra://-UT19xxZ7CziFps8ESFCUVSrOK2AnlrE4OifitLejts͏`׉ 7cassandra://U9TryloV32DNCQwo2GcBuEoWeAQaCdOnVxd2SXczX8M)>`j׉ 7cassandra://1WCsgFllPK2uxLKnNKwaSotgPbwIQE-ZgOK_HwyINkMLu͠ [ )C׉E GSources for mortality data The Human Mortality Database (HMD) was used for the data, supplemented by data from Eurostat for the years and countries for which no data was available in the HMD. For 2015, data from Statistics Netherlands was used as the data pertaining to the Netherlands. The information from these sources is regularly supplemented and is sometimes adjusted with retrospective effect for earlier years. The dataset used, in the form of mortality figures and exposures for both the Netherlands and the total group of West-European countries, can be found on the Association’s website and in total contains more than 100 million cases of death. The effect of these changes on life expectancy is made visible in chapter 8. 6.2 Assumptions of the model Most important assumptions of the model • The development of life expectancy in the Netherlands in the long term is based on the observed development of life expectancies in European countries with GDP above the European GDP average. • No separate cohort effects (including the effects of smoking behaviour) have been included because this increases the complexity of the model considerably. • For ages over 90, the mortality probabilities are extrapolated using the Kannistö method. • Only publicly available data have been used. Projection Model AG2014 is the point of departure The point of departure for the present model is the stochastic model used for Projection Table AG2014. This is a multi-population mortality model, as proposed by Lee and Li, with a two-stage approach to estimating the necessary parameters (see Appendix A). In addition, the European trend is estimated for each sex using the Lee-Carter model. The Lee-Carter mortality model is then used again to reflect the deviation of the Netherlands from the common trend. By combining the data from different, but comparable countries, a more robust model emerges with more stable trends and a smaller sensitivity to the calibration period used. The model is based on four stochastic processes: a) the development of mortality in Europe for men; b) the development of the deviation of mortality in the Netherlands relative to Europe for men; c) the development of mortality in Europe for women; d) the development of the deviation of mortality in the Netherlands relative to Europe for women; For developments a) and c) in Europe, a random-walk-with-drift model is used. For developments b) and d) in the Netherlands, a first-order auto-regressive process without a constant is used. The latter means that the development of mortality in the Netherlands is expected to follow the European trend in time. The four processes are estimated jointly in order also to estimate the correlations between the various processes. The joint implementation of this final step is a change relative to the estimation procedure used for Projection Table AG2014. For mortality in Europe, data up to and including 2014 is available and for mortality in the Netherlands data is available up to and including 2015. To estimate the four stochastic Projection Table AG2016 Mortality data and assumptions of the model 14 ׉ 7cassandra://U9TryloV32DNCQwo2GcBuEoWeAQaCdOnVxd2SXczX8M)>`j[ )C׉E processes together, it is necessary to apply the same historic data period. European observations for 2015 have therefore been extrapolated on the basis of the data available up to and including 2014 (see Appendix A). For higher ages (above the age of 90 years), there are relatively few observations. This can result in large fluctuations in the estimates of mortality probabilities. For this reason, the mortality tables are ‘closed’. This means that for ages over 90, the mortality probabilities are estimated using an extrapolation method. As in the case of the previous projection life table, the Kannistö method was chosen for Projection Table AG2016. Appendix A contains a full description of the stochastic model used, including the method used to estimate this model. In combination with the dataset. Projection Table AG2016 can be reconstructed exactly. Amendment relative to the model from 2014 The correlations between men and women are also included now in the estimates of the AG2016 model. In the previous model, the stochastic processes a) and b) for men mentioned earlier were estimated jointly, as were processes c) and d) for women. However, the processes for men, on the one hand, and women, on the other hand, were estimated separately from each other. In simulating future scenarios, the correlations between these processes were therefore set at nil. The data, however, suggests a positive correlation between the developments in mortality rates of men and women. Intuitively this is logical. It enhances the quality of the projection life table if these correlations are included in the estimate of the model. The modelling of the correlation between the four processes is improved by estimating them together and including all the correlations between the processes a), b) and d) referred to above. The correlations between the various processes are represented in the following diagram: European men -0.27 (AG2014: 0,51) 0.45 Netherlands deviation men 0.92 0.39 -0.21 (AG2014: -0.15) European women 0.57 Netherlands deviation women The correlation between (the annual changes in relation to) West-European men and the deviation of men in the Netherlands relative to West Europe is positive. In the case of women, this correlation is negative, but this does not mean that the correlation between changes in relation to West-European women and women in the Netherlands is negative. A negative correlation may be the consequence of changes in mortality in the Netherlands which generally have the same sign as changes in West Europe, but on average are less large. If there has been a large positive change in West Europe and a smaller positive change for the Netherlands, the difference (i.e. the change in the Netherlands less the change in West Europe) is, after all, negative. The effect of these changes on life expectancy has been made visible separately in chapter 8. Projection Table AG2016 Mortality data and assumptions of the model 15 [ )C[ )C{בCט{u׉׉ 7cassandra://b5_0WWbAswDrvscTwdKY9Qey8QEmWcZq69YqcFMhOuAB` ׉ 7cassandra://qaxXG7LasViYVOWxL8sZ0XPPurEqlDttnVhgvMYK7l4hA`׉ 7cassandra://hRpSTxL14ToCOvPLthJe9jCf_WlQV6dg-LU_1_JvdIsu`j׉ 7cassandra://rSDI74nZ5udlGv-Y_TDWbb4_4obyDM9tLUKUcNi54e0EXL͠ [ )C׉E6.3 Summary of the changes in the Projection Table AG2016 relative to AG2014 AG2014 Dataset including England and Wales, excluding the former East German AG2016 Dataset with the United Kingdom replacing only England and Wales and including the former East Germany from 1990 onwards Dataset for Europe up to and including 2009, forecast up to and including 2013 Dataset for the Netherlands up to and including 2012 and provisional data for 2013 Only the correlation between Europe and the deviation for the Netherlands have been included explicitly, not between men and women Dataset for Europe up to and including 2014, forecast for 2015 Dataset for the Netherlands up to and including 2015 All possible correlations between Europe and the deviation in relation to the Netherlands and between men and women which were included explicitly Projection Table AG2016 Mortality data and assumptions of the model 16 ׉ 7cassandra://hRpSTxL14ToCOvPLthJe9jCf_WlQV6dg-LU_1_JvdIsu`j[ )C׉E 7 UNCERTAINTY Following the publication of Projection Table AG2014, a number of interested parties in the sector posed the question whether the (stochastic) uncertainty resulting from that model was not too small. The Mortality Research Committee asked a number of experts explicitly for their views regarding the uncertainty in the model used. This did not result in proposals for adjustments to the model on the basis of explicit quantifiable scenarios, about which there was consensus amongst experts and which could be estimated using publicly available data. For this reason, the structure of the model has not changed. We have stated below precisely which uncertainty the model includes and which it does not include. 7.1 Extrapolation from the past In essence, the model used extrapolates not only mortality developments, but also the variability (volatility) of these. In other words, the mortality projections are based on the assumption that observed developments in the past, on average, will continue into the future. In the same way, the model also extrapolates the volatility in the development of mortality in the past. In other words, just as the parameters for the trend are estimated on the basis of observed developments in the past, so the same applies to the volatility parameters. In doing so, the AG2016 model, like the AG2014 model, gives an insight into the degree of volatility, as observed in the past in the development of mortality. Conceptually, of course, it is possible that the trend will be broken in 2017, which will cause this volatility to increase or fall. It is also possible for the trend to change permanently. In the projection, the Committee has opted to assume that a trend break such as this will not occur. A trend break such as this does not appear to have occurred during the past 40 years amongst the European population considered. The many positive medical developments and improvements in nutrition and lifestyles appear to have had a major, but gradual, impact. 7.2 No parameter and model uncertainty It is important to note that the uncertainty intervals presented in this publication do not take into account uncertainty in relation to parameters or the model. In other words, these intervals take the chosen model and the estimated parameters as the point of departure. The future deviations of the best estimate may be larger or smaller because mortality trends may occur which now cannot be foreseen, for instance due to exceptional medical and socio-economic developments. These developments may result in a future spread of mortality around the best estimate which may be different to the model-based spread calculated on the basis of historic data. Projection Table AG2016 Uncertainty 17 [ )C[ )C{בCט{u׉׉ 7cassandra://sCIYaRe_2GyZSC9gc2xdeLQv3GSx9VlJ2RI5pJUbTkkyW` ׉ 7cassandra://efpv20pTQ2PgECZ_vHxPt-sEWDA0QiS1Ub5IhD6HbSwp`׉ 7cassandra://RDhufeOWB1OfRCTNPaiaQkjfeRdsuwrkBmUzTYdRHGU `j׉ 7cassandra://oK6JekXZgCejvLXChojVhF5uNYZmsDTHPxYLogfs3LYXP|͠ [ )C׉EjIn the scientific literature methods are provided for formalising parameter and model uncertainty. In relation to parameter uncertainty, it can be noted that due to the enormous quantity of data (more than 100 million deceased with a total exposure of more than 11 billion) this may be expected to be small for a given model. Including model uncertainty requires the specification of a class of alternative models. There is only limited literature on this and for this reason it has been decided for the time being not to include this in this publication. 7.3 Distinction between uncertainty in mortality probabilities and uncertainty in mortality figures The above means that the uncertainty in the observed mortality figures will also be small. In addition to the uncertainty in the mortality probabilities, after all, there is also uncertainty in the actual number of people deceased in the light ofthese mortality probabilities. If, for instance, we consider a group of 100,000 people with a mortality probability of exactly 1% (on the basis of the assumption we have made of a Poisson distribution for individual mortality) the expected number of deceased is 1,000 and the symmetrical 95% confidence interval [938;1062]. This does not mean that the underlying mortality probability has suddenly become uncertain and has changed from 1% to an unknown value somewhere between 0.938% and 1.062%. It only means that we were not able to observe the mortality probability without measurement noise due to the small number of observations. The volatility in the mortality figures reported by Statistics Netherlands cannot therefore simply be used to make statements about uncertainty in the underlying mortality probabilities. The AG2016 model explicitly takes this into account in the estimation method. However, whoever wishes to estimate the future uncertainty in the pension or insurance portfolio must also take into account the uncertainty in individual cases of mortality after simulating the possible parts for future mortality probabilities. As a result, the distribution in portfolio results will increase. Projection Table AG2016 Uncertainty 18 ׉ 7cassandra://RDhufeOWB1OfRCTNPaiaQkjfeRdsuwrkBmUzTYdRHGU `j[ )C׉E@8 OUTCOMES This chapter gives the results of Projection Table AG2016. The results are compared with those of Projection Table AG2014. The effect on the level of the provisions has been calculated on the basis of a number of sample funds. With these sample funds, it is possible to assess of the effect on other pension funds. In addition, the AG2016 projection is offset against the historic developments and are placed in the perspective of the most recent projection of Statistics Netherlands (CBS 2015-2060).2 8.1 Observations in relation to AG2014 The overview below provides an insight into the AG2014 projection of life expectancy for 2014 and 2015 and shows how these life expectancies correlate with the observed life expectancies for the respective years. In addition, the table gives an insight into the projection of life expectancies for 2015 and 2016. Period life expectancy is used for this, since by doing so comparisons can be made for life expectancy in a specific observation year. Men 2013 2014 2015 2016 Observed 79.4 79.9 79.7 AG2014 79.5 79.7 79.9 AG2016 79.8 80.0 Table 1 Period life expectancy at birth Men 2013 2014 2015 2016 2 – Core projection 2015-2060: High population growth in the short term. Statistics Netherlands, December 2015 Projection Table AG2016 Observed 18.0 18.5 18.2 AG2014 18.0 18.2 18.3 AG2016 18.2 18.4 2013 2014 2015 2016 Table 2 Period life expectancy at the age of 65 The new observations since the AG2014 projection show a strong fall in mortality rates in 2014, as a result of which period life expectancy increases. In 2015, however, we see an increase in mortality rates, as a result of which life expectancy once again decreases. Outcomes 19 Women Observed 21.0 21.2 20.9 AG2014 21.0 21.1 21.2 AG2016 21.0 21.1 2013 2014 2015 2016 Women Observed 83.0 83.3 83.1 AG2014 83.1 83.2 83.4 AG2016 83.1 83.3 [ )C[ )C{בCט{u׉׉ 7cassandra://AM3_tIiJeeAFPnJIP5_rvsqYCgVigfkr5m2MqX8F1wk` ׉ 7cassandra://sLmvjty_cWmWWGv0a00WtZ1yqeE-BXCjwINW24yETUg|`׉ 7cassandra://0MWYFY10P1eh1j72N6wd5guDzRkrsEGQAerqqI-6MQg%e`j׉ 7cassandra://NN8J7fMR0eemR2pT8Oq56sUimAzewcko7Z15zsNvl50u]H͠ [ )C׉EiIn the next graph, the development of period life expectancy at birth is provided for the period up to and including 2050. Up to and including 2015, the graph is based on observed mortality figures and for the period thereafter on the AG2016 projection. Period life expectancy at birth 90 85 80 Women Netherlands 75 European selection AG2016 AG2016 Europe Men 70 65 1970 1980 1990 2000 2010 2020 2030 2040 2050 Graph 3 Period life expectancy for the Netherlands and selected European countries The fact that the period life expectancy of women in the Netherlands is still below the life expectancy of women in selected European countries, as it was in the previous projection is visible in graph 3. The life expectancy of men in the Netherlands, however, as in the case of AG2014, is above the life expectancy of men in the selected European countries. 8.2 From AG2014 to AG2016 To provide more insight into the differences between the former and the new projection life table, cohort life expectancy is used. All future mortality developments are included in the cohort life expectancy. The impact on cohort life expectancy for the start year 2016 is shown below step-by-step in relation to: 1. AG2014; 2. the inclusion of the correlation between men and women; and 3. the new dataset. Step AG2014 Correlation included Update dataset AG2016 At birth Men 90.1 -0.5 +0.5 90.1 Women 92.5 +0.6 -0.1 93.0 Table 3 Cohort life expectancy in 2016 The inclusion of the correlation between men and women results in the case of men in a decrease in life expectancy and in the case of women in an increase. The update of the dataset results in an increase in life expectancy in the case of men and a slight decrease in the case of women. The table shows that the life expectancy of men does not change on Projection Table AG2016 Outcomes 20 At the age of 65 Men 20.0 -0.1 +0.1 20.0 Women 23.0 +0.3 -0.2 23.1 ׉ 7cassandra://0MWYFY10P1eh1j72N6wd5guDzRkrsEGQAerqqI-6MQg%e`j[ )C׉E balance. In the case of women, life expectancy at birth increases by 0.5 years, while life expectancy in the case of women aged 65 increases by 0.1 per year. The point of departure of the model is that the mortality trend in the Netherlands is expected to converge towards the mortality trend in West-European countries of similar wealth. The present life expectancy at birth of men in the Netherlands is higher than that of men in West Europe. In the case of women, the opposite is true. Women in the Netherlands have lower life expectancy at birth than women in West Europe. The difference in life expectancy between women in the Netherlands and women in West Europe is greater than in the case of men. In addition, the mortality trend in the case of men is more in line with the West-European trend. This all contributes to the fact that women show a relatively strong improvement in life expectancy in comparison to men. The inclusion of the correlation between men and women apparently reinforces this effect. 8.3 Future life expectancy The Projection Table AG2016, as in the case of AG2014, offers the possibility of calculating future life expectancies. Future cohort life expectancies for the start years 2016, 2041 and 2066 are shown in table 4. Start year 2016 2041 2066 At birth Men 90.1 92.5 94.3 Women 93.0 95.1 96.6 Table 4 Future cohort life expectancy It once again appears from the figures stated above that the model implies that life expectancy for men and women will continue to increase, slightly more quickly for men than for women. As a result, the difference in life expectancy between men and women will fall. 8.4 Projection in perspective The developments in period life expectancy at birth for AG2014, AG2016 and CBS20152060 are compared in graph 4. The fact that the AG2016 projection for women in the Netherlands converges towards the projection for women in the selected West-European countries is visible. The AG2016 projection for men shows the same development as AG2014; the trend lies close to the trend in West-European countries, as a result of which the difference over time remains fairly constant. In the case of CBS2015-2060, a limited fall in life expectancy can be observed in the case of men compared to AG2016. Life expectancy in 2050 on the basis of CBS2015-2060 is slightly lower than in the case of AG2016. difference 2.9 2.6 2.3 At the age of 65 Men 20.0 23.2 25.7 Women 23.1 26.2 28.4 difference 3.1 3.0 2.7 Projection Table AG2016 Outcomes 21 [ )C[ )C{בCט{u׉׉ 7cassandra://FuuMY_FBqrb-kwr85i0u4ld8JrhXhQK1gp2mKvTb05IV` ׉ 7cassandra://fw8ZMCj5vaKYyO3D_ZCXoTJo5_gtjQNcvEsFnWn2gi0͈2`׉ 7cassandra://NkX4dKC0CLYk2hOpcYOaM41kIJcAiuGWIe777nOeE5k'`j׉ 7cassandra://AGeLeIpgEDr8Qoj-UMm5_N28ViDRIfRc7yX8n3ExEg4ʹ͠ [ )C׉EPeriod life expectancy at birth 90 85 Women Netherlands 80 European selection AG2016 AG2016 Men 75 2000 2010 2020 2030 2040 2050 Graph 4 Development of period life expectancy at birth Graph 5 shows the development of period life expectancy at the age of 65. Period life expectancy at the age of 65 30 AG2016 Europe CBS2015 AG2014 25 20 Women Netherlands 15 Men 10 1970 1980 1990 2000 2010 2020 2030 2040 2050 Graph 5 Development of period life expectancy at the age of 65 The cohort life expectancies for AG2014, AG2016 and CBS2015-2060 are stated in table 5. The differences in cohort life expectancy at the age of 65 between AG2016 and CBS20152016 are small. Prognosis AG2014 AG2016 CBS2015-2060 At birth Men 90.1 90.1 Women 92.5 93.0 Not available At the age of 65 Men 20.0 20.0 20.1 Women 23.0 23.1 22.7 Table 5 Cohort life expectancy at birth and at the age of 65 for the year 2016 Projection Table AG2016 Outcomes 22 European selection AG2016 AG2016 AG2016 Europe CBS2015 AG2014 ׉ 7cassandra://NkX4dKC0CLYk2hOpcYOaM41kIJcAiuGWIe777nOeE5k'`j[ )C׉E8.5 Link between life expectancy at the age of 65 and the retirement age in the first and second tiers The Raising of the State Pension Age and Standard Pension Retirement Age Act (Wet verhoging AOW-en pensioenrichtleeftijd) of 12 July 2012 links the retirement age in the first tier (the state old-age pension or ‘AOW’) and the standard retirement age in the second tier (the employer’s pension) to period life expectancy. In accordance with the Act of 4 June 2015 in relation to the accelerated gradual increase in the State Pensions age3, a decision must be taken at the latest on 1 January 2017 to determine whether the State Pension age is increased in 2022 from 67 years to 67 years and three months. Increases in the retirement age take place in steps of three months and depend on the level of the macro average remaining period life expectancy at the age of 65 (L), as estimated by Statistics Netherlands relative to a value of 18.26 and the difference between the retirement age applicable up until that moment and 65 years. The reference value of 18.26 has been determined by law and is based on observations of Statistics Netherlands in the period 2000-2009. If it is expected that L for 2022 will be greater than 20.51 years, an increase in the commencement date of the state old-age pension by a quarter of a year (0.25) is necessary (after all, (20.51 – 18.26) – (67 – 65) = 0.25). According to Projection Table AG2016, L will indeed exceed this value in 2022. This expectation is in line with the most recent projection by Statistics Netherlands from 2015 and a decision will have to be taken in respect of this increase in 2022 at the latest on 1 January 2017. After this, the same method will be applied annually, whereby it will be necessary to determine whether an increase in the State Pension age pension by a quarter of a year will or will not take place. If the macro average remaining period life expectancy at the age of 65 years is also estimated for the years after 2022, the following years are determined in which the commencement date of the state old-age pension is expected to increase by a full year. To simplify the calculation, the macro average remaining life expectancy is determined below as the weighted average of the life expectancy of men and women. In practice, a more exact weighting may possibly be assigned, as a result of which women will be assigned a slightly higher weighting. The impact of this is small. Commencement date of the state old-age pension (AOW) 68 69 70 71 3 – In full: Act of 4 June 2015 amending the General Old-age Pensions Act, the Salary Tax Act 1964, the Raising of the State Pension Age and Standard Pension Retirement Age Act, the Obligatory Occupational Pension Scheme Act and Other Fiscal Measures in 2015 in Relation to the Accelerated Gradual Increase in the State Pension age. Projection Table AG2016 CBS2015 2029 2036 2045 2054 AG2016 2027 2035 2044 2053 Table 6 Estimate of the development of the State Pension age The increase in the standard retirement age in the second tier is based on the same formula as the State Pension age, although, in accordance with the Act, it is necessary to anticipate an expected increase in life expectancy at an earlier stage. It is a legal requirement that a change to the standard retirement age must be announced at least one year prior to this change taking effect and that for this purpose the macro average remaining life expectancy at the age of 65 must be taken into account that is expected 10 years after the calendar year in which the change is made. This means, for instance, that an change to the standard retirement age in 2018 must be announced before 1 January 2017 on the basis of the macro average remaining life expectancy at the age of 65 in 2028. Outcomes 23 [ )C[ )C{בCט{u׉׉ 7cassandra://oflkncrJL4pAT10DuKdk4_OzlihFFy1T1U-2_TSOFsg` ׉ 7cassandra://cMvWwHceRjEZRQmHyvAhaNsGY9uhMhWrZArtYoB0V5Y͔7`׉ 7cassandra://DyLhqXW2iWP-ze5gDqDfW39M0GbTcnISwk9gMttSSWk*[`j׉ 7cassandra://HGU7x6aaOXUWLYfb4A4U95JyYswpDApSXhqUjFDHou4Y͠ [ )C׉E [On the basis of the Projection Table AG2016, L is expected to increase to such a degree that in 2018 a standard retirement age of 68 years will apply. The most recent projection by Statistics Netherlands dating from 2015 shows that this increase will be necessary in 2019. At the latest on 1 January 2017, in accordance with the Act, a decision will have to be taken with regard to any increase in the standard retirement age in 2018 on the basis of the most recent forecast by Statistics Netherlands. In general, it can be concluded that the Association’s present projections do not deviate much from the projections by Statistics Netherlands, as a result of which the present expectation is that differences in future State Pension age (AOW) and retirement pensions will not be very great. 8.6 Effects on the provisions In order to analyse the effects of Projection Table AG2016 on the technical provisions of pension portfolios, six sample funds were constructed. These are three funds with male members and three funds with female members. For each sex, a young, old and average fund was constructed. The last fund is the average of the first two funds. These sample funds were determined partly on the basis of concrete portfolios. In addition to a retirement pension, the sample funds contain a latent survivor’s pension and a survivor’s pension in payment. In the case of the male portfolios, it is assumed that payments of the survivor’s pension in payment relate to female partners. In the case of the female portfolios, the opposite is the case. The types of pension used are a retirement pension, commencing at the age of 65, and a survivor’s pension of the ‘unspecified partner’ form with a partner frequency of 100%. A fixed age difference of three years between the male and female partner is assumed, whereby it is also assumed that the male is older than the female. The actuarial discount rate applied amounts to 3%, so that the effects are comparable to the previous publication (AG2014), in which an interest rate of 3% was assumed. Cover RP (65) SP RP+SP Men Young -0.1% 1.4% 0.3% Average -0.2% 1.1% 0.2% Old -0.2% 0.8% 0.1% Women Young 1.0% -1.6% 0.6% Average 0.7% -1.0% 0.5% Old 0.6% -0.7% 0.4% Table 7 Impact on the provisions (actuarial discount rate 3%) for the model portfolios for the transition from AG2014 to AG2016 (difference AG2016 minus AG2014, expressed as a percentage of AG2014). The separate percentages, as stated in relation to the types of pension, retirement pension and survivor’s pension, do not add up to the percentages, as stated in the combination of a retirement pension and survivor’s pension. This is because the provisions of the various types of pension are different. ■ RP = retirement pension SP = survivor’s pension Although the retirement age has now been increased to 67 years, large parts of the pension liabilities are still based on a retirement age of 65. It is possible to conclude from table 7 that the differences, in terms of the provision, are small in the case of men. In the case of an average dataset, the provision increases by approximately 0.2%. In the case of women, the impact is greater (an average increase of 0.5%). Depending on the composition of the pension fund, the increase will amount to a minimum of 0.1% and a maximum of 0.6% on the basis of an actuarial discount rate of 3%. Projection Table AG2016 Outcomes 24 ׉ 7cassandra://DyLhqXW2iWP-ze5gDqDfW39M0GbTcnISwk9gMttSSWk*[`j[ )C׉EGiven the present low interest rate, we have also provided an indication of the effects on the basis of a fixed interest rate of 1% in table 8. The interest rate has an impact on the ultimate effect due to the long-term liabilities. In the case of an actuarial discount rate of 1%, the low interest rate results in an additional increase in the impact. Cover RP (65) SP RP+SP Men Young -0.1% 1.8% 0.4% Average -0.1% 1.5% 0.3% Old -0.2% 1.1% 0.3% Women Young 1.3% -2.1% 0.9% Average 1.1% -1.4% 0.7% Old 0.9% -1.1% 0.6% Table 8 Impact on the provisions (actuarial discount rate 1%) for the model portfolios for the transition from AG2014 to AG2016 (difference AG2016 minus AG2014, expressed in AG2014). The separate percentages, as stated in relation to the types of pension, retirement pension and survivor’s pension, do not add up to the percentages, as stated in the combination of a retirement pension and survivor’s pension. This is because the provisions of the various types of pension are different. ■ RP = retirement pension SP = survivor’s pension These sample funds contain a combination of rights to a retirement pension and a partner’s pension. Tables 9, 10 and 11 show the effect on the provision for these various types of pension. Retirement pension (65 years) Men -0.2% -0.1% -0.1% -1.0% Age 25 45 65 85 Actuarial discount rate 3% Actuarial discount rate 1% Men Women 1.5% 1.1% 0.2% -0.8% Retirement pension (65 years) Actuarial discount rate 3% Actuarial discount rate 1% Age 25 45 65 85 Men 3.2% 2.5% 1.2% 0.1% Women -6.0% -2.4% -0.1% -0.8% Survivor’s pension in payment Actuarial discount rate 3% Actuarial discount rate 1% Age 25 45 65 85 Men 0.3% 0.4% 0.2% -0.8% Women 0.0% -0.1% -0.1% -1.0% Men 0.6% 0.6% 0.3% -0.9% Women -0.1% -0.1% -0.1% -1.0% Tables 9, 10 and 11 Impact on the provisions (actuarial discount rate of 3% and 1%) for the various types of pension and ages in the transition from AG2014 to AG2016 (difference AG2016 minus AG2014, expressed as a percentage of AG2014) In the case of higher pension ages (for instance, 67 years), the effects are almost the same as those based on a retirement age of 65 years. Projection Table AG2016 Outcomes 25 Men 3.6% 2.8% 1.4% 0.0% Women -6.0% -2.6% -0.3% -0.9% -0.2% -0.1% -0.1% -1.0% Women 1.8% 1.3% 0.3% -0.9% [ )C[ )C{בCט{u׉׉ 7cassandra://5rVRrj7vsAZZG2cB8sbnWoQo0gflaHnDNhvB9wnlbNw` ׉ 7cassandra://Llgq8q43vSDjTlCxLIk7sbRtFSAZWFWKztEueNAiTMI͐`׉ 7cassandra://JfkIjMaVZnfR4FKDCo8gUHcekoF8avDAagfqFHQW-yE(`j׉ 7cassandra://0vGeWk19UEnuKMKoUYbz5f4eZNqgefN_4l046XCUZBQX̆͠ [ )C׉E 9 APPLICATIONS OF THE MODEL The use of a stochastic model offers opportunities in relation to the analysis of mortality risks. In particular, it is possible to obtain an insight into the variability of the value of the liabilities of insurance portfolios. Since the Projection Table AG2016 is based on a stochastic model, it is possible to draw conclusions on the spread of future mortality probabilities around the best estimate. In essence, the model used extrapolates not only mortality developments, but also the variability (volatility) of these. This volatility is consequently representative of uncertainty, such as occurred in the past. It is important to note that the uncertainty intervals presented in this publication do not take into account uncertainty in relation to parameters or the model. In other words, these intervals take the assumed model and the estimated parameters as the point of departure. In this chapter, several possible applications of the stochastic model are mentioned by way of illustration. The results stated in this chapter are based on the same model portfolios as those referred to in chapter 8. In the first application, we consider the value of the liabilities for all possible developments of future mortality probabilities. Where the best estimate value of the liabilities can be estimated by using the best-estimate mortality probabilities, we have considered the possible development in mortality probabilities on the basis of the likelihood that they will occur, as shown by the stochastic model. This gives an insight into the possible increase in the total run-off of liabilities, for instance, in the 95% quantile. A second application relates to the stochastic distribution of the best-estimate portfolio value, based on an horizon of 1 year. In this regard, consideration is only given to possible shocks during the first year and the best estimate is subsequently used. In other words, shocks in subsequent years are set at nil. This application shows what can happen in a year and the increase in the liabilities which results from this. Finally, we show a third application in which the stochastic model is used to determine confidence intervals in relation to life expectancy. In case of the above applications, no conclusions are drawn with regard to the consequences for the calculation of the buffers created in accordance with Solvency II. Basing the amount of capital to be tied up for mortality risk exclusively on the distribution resulting from the stochastic model could result in underestimating the required capital. The stochastic model, after all, does not take into account parameter uncertainty, nor model uncertainty. Projection Table AG2016 Applications of the model 26 ׉ 7cassandra://JfkIjMaVZnfR4FKDCo8gUHcekoF8avDAagfqFHQW-yE(`j[ )C׉E 9.1 Simulating the value of the liabilities The best-estimate value of the liabilities can be obtained by assuming that future mortality probabilities will develop according to the model comparisons in Appendix A, whereby all disturbances are set at nil. It is also possible to simulate scenarios in which the disturbances are generated stochastically by means of a multivariate normal distribution. Table 12 gives as an example for 10,000 such scenarios the average and the quantiles for 95%, 97.5% and 99.5% for the Pension Liabilities Provision. For this purpose, the average model portfolios comprising men and women are used with a fixed actuarial discount rate of 3% and 1%. The outcomes are expressed relative to the best-estimate values. Outcomes of the simulation for the provision for pension liabilities (in relation to the best estimate) - 3% interest RP Standard deviation Quantiles 50% 95% 97.5% 99.5% 2.2% 100.0% 103.6% 104.2% 105.4% Men SP 1.6% 100.0% 102.6% 103.2% 104.2% RP + SP 1.3% 100.0% 102.2% 102.5% 103.3% RP 1.5% 100.0% 102.5% 102.9% 103.9% Women SP 2.0% 100.0% 103.3% 104.0% 105.3% RP + SP 1.3% 100.0% 102.1% 102.5% 103.3% Table 12 Results of the simulation of provisions based on 3% for model portfolios (men and women averaged) ■ RP = retirement pension SP = survivor’s pension In the case of a 1% actuarial discount rate, the distribution in the results is greater. Results of the simulation of provisions based on 1% for model portfolios (men and women averaged) RP Standard deviation Quantiles 50% 95% 97.5% 99.5% 2.7% 100.0% 104.4% 105.2% 106.7% Men SP 1.8% 100.0% 102.9% 103.6% 104.7% RP + SP 1.7% 100.0% 102.7% 103.2% 104.2% RP 1.9% 100.0% 103.1% 103.6% 104.7% Women SP 2.6% 100.0% 104.3% 105.2% 107.0% RP + SP 1.7% 100.0% 102.7% 103.2% 104.2% Table 13 Results of the simulation of provisions based on 1% for model portfolios (men and women averaged) ■ RP = retirement pension SP = survivor’s pension The distribution resulting from the simulations strongly resembles a normal distribution. As is apparent from the above tables, the spread of the various types of pensions is considerably higher, in particular in the case of the retirement pension for men and the survivor’s pension for women. Simulations based on Projection Table AG2014 show a comparable distribution for the retirement pension, but the survivor’s pension results in a much higher standard deviation: in the case of an actuarial discount rate of 3%, this is equal to 3.4% in the case of AG2014, as compared to 1.6% in the case of AG2016. This considerable reduction relates to the inclusion of the correlation between the mortality of men and women in the AG2016 model. Projection Table AG2016 Applications of the model 27 [ )C[ )C{בCט{u׉׉ 7cassandra://VtpR5juK-JFw3YPkNQ4n07nK1cbhDNeIn_aAhOsDwOQ` ׉ 7cassandra://7UU9Dfe-B07g9cm1FZOd-GDFthipXNXX2B9hqPK7dVYr `׉ 7cassandra://RLlZSEGZXJGXW1YWLZx1Lxpv6Kdo28fqKudRS6guLzo$`j׉ 7cassandra://eByyci8VtTVex3PiEefi8sofcJPPlbU8-nsV_ptraig͖_30͠ [ )C׉E+Since the correlation for the European trend is large and positive (about 90%), compensatory effects arise in the simulation when determining the value of the Provision for Pension Liabilities for the survivor’s pension. By way of illustration, graphs 6 and 7 show the distribution of the simulated values for the retirement pension, survivor’s pension and the combination of both types of pension relative to the best estimate. This relates to the model portfolio for men (average) and an actuarial discount rate of 3%. Graph 6 shows the distribution for AG2016, graph 7 for AG2014. Distribution of the Provision for Pension Liabilities in accordance with AG2016 Combination Survivor’s pension Retirement pension 85% 90% 95% 100% 105% 110% 115% Graph 6 Distribution of outcomes for the simulation of the provision (actuarial discount rate 3%) for the model portfolio of men (average) around the best estimate Distribution of the Provision for Pension Liabilities in accordance with AG2014 Combination Survivor’s pension Retirement pension 85% 90% 95% 100% 105% 110% 115% Graph 7 Distribution of outcomes for the simulation of the provision (actuarial discount rate 3%) for the model portfolio of men (average) around the best estimate in accordance with AG2014 Projection Table AG2016 Applications of the model 28 ׉ 7cassandra://RLlZSEGZXJGXW1YWLZx1Lxpv6Kdo28fqKudRS6guLzo$`j[ )C׉E*9.2 Simulating the best-estimate value in a year’s time An alternative measure of uncertainty arises if one is interested in the distribution of the best-estimate value of the portfolio with an horizon of 1 year. This arises from a calculation of the best estimate for 2017, after simulating the uncertainty of the coming year (in other words, simulation of the disturbances for t=2016). All the disturbances for the years after 2016 are therefore set at nil. The results of this are stated in the table below. One-year shock (in relation to the best estimate) Men 1% Standard deviation Quantiles 50% 95% 97.5% 99.5% 0.4% 100.0% 100.7% 100.8% 101.1% 3% 0.4% 100.0% 100.6% 100.7% 101.0% Women 1% 0.4% 100.0% 100.6% 100.7% 100.9% 3% 0.3% 100.0% 100.5% 100.6% 100.8% Table 14 Results of the one-year simulation of provisions (actuarial interest rate of 1% and 3%) for model portfolios (men and women averaged) These outcomes show that the spread in the case of a one-year simulation is much lower, as might be expected) than in the case of a simulation for all years. 9.3 Simulating life expectancy Finally, we show applications here of the stochastic model in which the simulated scenarios are used to reflect the uncertainty in the projection of life expectancy. Period life expectancy at birth 90 85 80 Women 75 Observations Netherlands 95% confidence interval Men 70 Observations European (selection) Projection Netherlands Projection European selection 65 1970 1980 1990 2000 2010 2020 2030 2040 2050 Graph 8 Confidence interval in relation to the best estimate of the period life expectancy of men and women in the Netherlands Graph 8 shows that the uncertainty in the projection of period life expectancy, as expected, increases as the projection lies further in the future. Projection Table AG2016 Applications of the model 29 [ )C[ )C{בCט{u׉׉ 7cassandra://dugyM6RhEzNe4EIPPQwTTbxXtgDWfbEf5OSUP1xiOEk 1` ׉ 7cassandra://AQi2MYVcRjNcA_995F-B8geL-OWOxv8jDxLwI833i2MD`׉ 7cassandra://yQ6fJIbo-z9oimQh6-6kbh1tIgfWyHDvB2aIJ4UhfxU*`j׉ 7cassandra://vJhc-ur18L_6AD-7avIAu_QC5UrUC2MVt2ygMIil-LY"' ͠ [ )C׉EGraph 9 below shows the uncertainty in cohort life expectancy of men and women in the Netherlands in 2016. Life expectancy of the population of the Netherlands 2016 105 100 95% confidence interval Women Men 95 90 85 80 0 10 20 30 40 50 60 70 80 90 100 Present age Graph 9 Confidence interval around the best estimate of cohort life expectancy for men and women in the Netherlands in 2016 Graph 9 shows that the uncertainty decreases as age increases. This is due to the fact that the number of years for which an estimate is made decreases as age increases. In addition, the fact that life expectancy first decreases up to an age of approximately 60 years and then increases is visible. Two effects play a role in this. A person who is older has already survived a period, as a result of which life expectancy increases with age. In addition, someone who is younger will benefit more from expected future improvements in mortality. It should be noted that in the confidence intervals shown we only take into account uncertainty in future mortality probabilities and do not consider individuals. Since the mortality probabilities for (for instance) a 90-year-old change little over time, we observe hardly any differences in his or her expected age at death if we simulate all sorts of possible future scenarios with our model. However, this means, of course, that the moment of death of an individual 90-year-old is known now. Little uncertainty in mortality probabilities above this age does not imply, after all, that there is little uncertainty about the actual moment of death for an individual. Projection Table AG2016 Applications of the model 30 Life expectancy ׉ 7cassandra://yQ6fJIbo-z9oimQh6-6kbh1tIgfWyHDvB2aIJ4UhfxU*`j[ )C׉E&APPENDICES Projection Table AG2016 31 [ )C[ )C{בCט{u׉׉ 7cassandra://dX8yi5RMSIyCOvunBudw79AU5k7sBqVlVenrzXwTLtoU` ׉ 7cassandra://zjxu4anDHtmeCZWcy19COcMq5L9lWoIDdGGHJmbDG8Qj.`׉ 7cassandra://qx0g8ecahPHVC-aI_c7byDUZmR0l-FaYxh790Bkjecw `j׉ 7cassandra://NM1g0LWQsgzbi8NFmxJxkd67jH_cmplZBhgdqnaYuYo[̦͠ [ )C׉E 8APPENDIX A Projection Model AG2016 Technical description 1. Terms and definitions The projection table shows per sex for the ages      and years        the best estimate for the one-year mortality probabilities . This is the probability that someone who is alive on 1 January of year t and who was born on 1 January of year    will be deceased on 1 January of year  . The model also allows the user to draw up a projection for the years after 2066. The mortality probabilities are not modelled immediately; instead we specify the corresponding force of mortality (or 'hazard rate') . We assume that    for all     1. As a result of this         Each dynamic model that is described in terms of the force of mortality  can therefore be described in terms of one-year mortality probabilities using the above formula. 2. Dynamic model For ages up to and including 90 years,      with    , the Li-Lee1 model is used for both sexes   :                       with a trend factor for each sex, age   and years    defined by the time series             where   is the force of mortality for the population of the Netherlands (with sex ),  force of mortality for a peer group of West-European countries and   the  the quotient of the two (i.e. the deviation for the Netherlands relative to the peer group). This means that a random walk with drift model is assumed for the time series of the peer group and a first-order autoregressive model, without a constant term, for the time series of the deviation for the Netherlands. The stochastic variables        are independent and identically distributed (i.i.d.) and have a four-dimensional normal distribution with a mean (0,0,0,0) and a given 4x4 covariance matrix .   1 Li, N. and Lee, R. (2005) Coherent Mortality Forecasts for a Group of Populations: An Extension of the Lee-Carter Method. Demography 42(3), pp. 575-594. Projection Table AG2016 Appendix A 32 ׉ 7cassandra://qx0g8ecahPHVC-aI_c7byDUZmR0l-FaYxh790Bkjecw `j[ )C׉E 3. Closure of the table For ages above 90 years,      with     , the Kannistö closure method is used, which is based on a logical regression using the table for ages     . The number of ages  on which the regression is based is therefore , the average of these ages is        and the sum of the squares of the deviation is      Closure using the Kannistö technique means that for                          .  . where  and are respectively the logical and inverse logical functions.   and the regression weights are given by             If a mortality probability is required for an age greater than 120, it is assumed to be equal to the mortality probability for the age of 120. 4. Best estimates for mortality probabilities and life expectancy Since we identify the best estimates for future values of the time series with the most likely outcomes, these correspond to the series for   and  , which are obtained by filling in        for all values of . The covariance matrix  is therefore not required to generate these best estimates, but is necessary to carry out simulations which may help in analysing uncertainty in relation to the best estimates.                under the assumption that this person was born on 1 January of year   (with    and   ) and assume that someone who dies within a calendar year on average is still alive during the calendar year for six months, we find for this so-called cohort life expectancy:             Note that according to this         The probability that the person at time   is still alive is, after all, the product of mortality probabilities    for all years s between  and , whereby every year the person not only ages by a year older, but we also have to take into account on each occasion a new column in the mortality table. This last effect is not included in the period life expectancy:            which suggests that the mortality probabilities of today (time ) will no longer change over time. This results in an incorrect impression of life expectancy and although this period life expectancy is often      , this is incorrect. Projection Table AG2016 Appendix A 33     [ )C[ )C{בCט{u׉׉ 7cassandra://aTk5Z8ydvzTzOwrOLvVZnogqUCBhCDDzpwkCVWYegoUO-` ׉ 7cassandra://belitPSlUiw-DViZYCocJeSYtA8soWqdtZ9gqcdFei0w`׉ 7cassandra://XjC_GFTS8kAQFDUbom07aP8SzPHKYUfq-a6rDJXBjpU#i`j׉ 7cassandra://ds1XvT7iY7cYgW7DF2nrZ3aEK2SzG0L5244rZcAYi34͠ [ )CÔנ[ )C)ҁ 9ׁH8http://www.mortality.org/Public/Docs/MethodsProtocol.pdfׁ ׁ Јנ[ )C 9ׁHFhttp://statline.cbs.nl/Statweb/publication/?DM=SLNL&PA=37168&D1=a&D2=1ׁ ׁ Јנ[ )C 9ׁH+http://ec.europa.eu/eurostat/web/populationׁ ׁ Јנ[ )Cj 9ׁH+http://ec.europa.eu/eurostat/web/populationׁ ׁ Ј׉E 5. Dataset used for calibration The parameter values in the model are determined using maximum likelihood. In doing so, mortality figures and exposures in West-European countries and in the Netherlands were used. In all cases it was assumed that for the given exposures  the observed deaths2  have a Poisson distribution and that the expectation of  is equal to the force of mortality  to be modelled. We have suppressed sex and the designations EUR/NL in this notation. The table below shows which data source was used per geographic area and per year as the input for the AG2016 model. The data from the Human Mortality Database (HMD) was supplemented for the years after 2011 by data from the Eurostat database3 (EUROS). For the Dutch data for 2015, the database4 of Statistics Netherlands was used (Statline). In the last two databases, we find the required numbers of deaths per sex but not the exposures. However, these can be deduced from other quantities which are given:  : the population on 1 January in the year  aged between  and    : the number of people who died in the year , who would be between  and +1 years old on 31 December of year . Conversion to exposures occurs using the method determined in the protocols5 of the Human Mortality Database. This gives for  :    and for  :                     2 Brouhns, N., Denuit, M. and Vermunt, J.K. (2002) A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics 31, pp. 373-393. 3 demo_pjan (population P) downloaded on 03/03/2016 from: http://ec.europa.eu/eurostat/web/population-demography-migration-projections/population-data/database and demo_mager (sterfte C) / demo_magec (sterfte D) downloaded on 18/03/2016 from: http://ec.europa.eu/eurostat/web/population-demography-migration-projections/deaths-life-expectancy-data/database 4 Definitive mortality figures for 2015, see http://statline.cbs.nl/Statweb/publication/?DM=SLNL&PA=37168&D1=a&D2=1-2&D3=0%2c56162&D4=0&D5=60-64&HDR=G3%2cT%2cG1&STB=G2%2cG4&VW=T 5 See http://www.mortality.org/Public/Docs/MethodsProtocol.pdf Projection Table AG2016 Appendix A 34 ׉ 7cassandra://XjC_GFTS8kAQFDUbom07aP8SzPHKYUfq-a6rDJXBjpU#i`j[ )C׉E6. Calibration method The following three steps are taken separately for the two sexes  :  We take the exposures  ,   and    with                        and observed deaths   for the relevant Western European countries, with      and    . This concerns in all cases the sum of all exposures and the sum of all deaths in the respective countries, including the Netherlands. The parameters   were then determined in such a way that the Poisson likelihood function for the observed deaths is as large as possible for the given exposures:         requiring the sum of the elements of  elements of  . To obtain a unique specification of the three vectors we normalise by  over   to be equal to  and the sum of the  over   to be equal to .  Data after 2014 are not available for all the relevant countries. For this reason, the values of  then applied        en  , by means of    with                     The maximum likelihood method is now applied to the data for the Netherlands to determine             as previously. Once again, normalisation takes place by requiring the sum of the elements in   over  and  In a fourth and final step, the four time series are used, namely       ,    (now including the year 2015) and  over   to be respectively  and .     the parameters  and matrix . On the assumption that the variables     are independently and identically distributed and have a four-dimensional normal distribution with average (0,0,0,0) and covariance matrix , we select the estimators for  and  in such a way6 that the likelihood of these time series is maximised. 7. Simulation of the time series In order to be able to simulate the scenarios for the timeseries         to estimate            in the previous step are determined up to and including 2014. Linear extrapolation is     , samples from a normal distribution with an average of (0,0,0,0) and covariance matrix C must be generated. This can be done by multiplying a (row) vector  with four independently standard normally distributed variables by a matrix H, which satisfies the condition  , in other words by means of  . In the list of parameters in the publication and the accompanying Excel spreadsheet, a Cholesky H matrix has therefore also been included in addition to the covariance matrix C. 6 The working group made use of the R package, systemfit, for this with the options method=”SUR” and methodResidCov=”noDfCor”. Projection Table AG2016 Appendix A 35 [ )CŁ[ )Cā{בCט{u׉׉ 7cassandra://GESOx6c1d3BSBIvwD_zsfMVPg5iR6iwitp9LH47FIKU` ׉ 7cassandra://-CgGvTGZMgbkyU2NBYVDLA7jvH8iIsEw81FphmtNCro̓H`׉ 7cassandra://X97HWfhZzTzJvofMRyO-IpBeltHnS4TZhN8fg-mtSzo!`j׉ 7cassandra://GKdrptqSWVdAV3dpPR1KsFDPFJRsHWaLxNM_UFry2ogwͥ͠ [ )C׉EParameter values aHFW U V T c p q r V T c p q r V T c p q r V V V VV VT Vc V Vp Vq Vr T T T TV TT Tc T Tp Tq Tr c c c cV cT cc c cp @UB !@UB ( '(@UB IT2qcTcVqT2TVcp I2VTrqp Ip2TTqpc2qrqrpq Ip2qprpc2rrqqpp Iq2rrTq2Vq )&(@UB 2qcTp 2TcqrVp I2Tccq 2qrqpq I2TprVrc 2VpTcq I2qVpVT Iq2VcVTrq2TVrqT I2crTqpc I2qpVqV Iq2TTTVpp2rpp 2VcVrcqc 2TrT Iq2Tqcrrp2VqV I2TprcTV I2crrcp Iq2cTpVT2rqVTV 2TTc I2cppVrp Iq2cqTTTcc2rT I2qqTp I2TVVpc Iq2VqrrTVc2TcTV I2rqpVr I2qTpr Iq2VrrVrpp2rprV 2TcTrpV 2rqr Iq2TqT2qTrq I2pVVTcV I2rVrc Iq2ccTVcVc2TTq I2rTqp I2rqVc Iq2TTTr2crqqq I2qpVr Iq2qVrT2cqrr I2Vcq 2VqVcV 2qrV Ip2rVVpT2TqqqppT I2qTqprT I2VTrpcq Ip2cVrpq2cpT I2crTT 2VTq Ip2crcc2ccqrV I2rTVcpT I2ccpc I2rcVpcVr2Vcprr I2TcVrTrr I2pp I2qqqc2VTpqp I2TTcq I2VV I2qpcrqcp2rVVVT I2TrrVVVq I2pc I2qppTV2pqTp I2VrpVVT I2rpcpqpc I2qqVVpV2cpcrqq I2Tp I2Tcp I2qrVTqrqr2rVTTcqr I2Vqccp I2rTpTV2qqVr I2VqppTVpq I2rqqVrT2qcccq I2VrrT I2rrcpqV2prcT I2VrVTTq I2qrqpprr2pprVVT I2TVqcpr I2qpqcVcpT2pTrVV I2TVTr I2qTVTVV2pcp I2VqcTVVrq I2qV2pcp I2Tpqq I2ppcrrVrV2pTTTT I2VqpTqT I2pVVr2pVqcc I2VqcVcrp I2qVVrc2ppTV I2VqVpcV I2TTcqr2pqcr I2VrrqqqVc I2ccqcccq2ppqpcc I2VpqcqpVp I2TqqcT2prc I2VqTcpqV I2TTcp2qVqp I2VqcVTp I2VVV2qVrVT I2VqVqrqT I2TTVTr2qVTpc I2VpcVT I2cqr2qcqc I2VprVppT I2VqTc2qVVqV I2Vrrrrr Ic2rqqcp2qqTpp I2VcVpV Ic2qpTccT2qqTqrr I2VVrTVcpr Ic2ppqrVc2qqrqqq I2VVqTVqr Ic2pprrTcT2qqppq I2VTprcc I2prVcpT Ic2cqVqTrrTr2qqrVqr I2VqrT I2pcpV Ic2TqpVTV2qqVTT I2rVprTcT 2VT Ic2VrVcpT2qqqV I2qrrp I2TrTpV Ic2rTVc2qqcV I2pqppV I2VTrq Ic2rcrqrq2rrT I2qTqVp I2Vqr Ic2rVcVq2qpqVpV I2cTcTr I2pTcrT Ic2rrppp2qqVpp I2Vqrrp I2qTppV IT2rcVpcpV2qqTpT I2qVTc I2VrVc IT2qrVVV2qqpqr I2TTpVT I2VVcVq IT2pqqr2qrrpqq I2rcq I2cprq IT2VqcpTT2rrVV I2qcTpVT I2pV IT2cTTrrqqV2rTTrq I2crccqV I2rT &&( I2qpr ( 2rprqV & 2rT 2Vqqqq 2rpc 2pqcq 2qrp 2Vrprr 2Vrp 2crTVV 2pqpT 2qqqq 2Vrqpcq 2VTTcqVr 2TrTq 2cVqpq 2rpprr 2cVc 2ppcVqr 2Vcc 2qV 2TVprV 2qprpq 2qrTcr rp rp rp rpV rpT rpc rp rpp rpq rpr rq rq rq rqV rqT rqc rq rqp rqq rqr rr rr rr rrV rrT rrc rr rrp rrq X@&B Vr2rTrp Vp2qTpqq Vp2qVT V2qVrVrp VT2TVccqrcq VT2TTpVTVr VV2Tppp q2qTcT r2VqTVTr p2TrVpq c2ppqcp T2rrrrV 2rTrTpp 2TprrpT p2qqrc p2rVTVpVcr c2qcTcVq 2qVcrVVcV r2rVTprr q2ccVcr q2Vrqcp 2prqr V2pcppq V2qccrp I2TVcTqrpT I2qcrpTc IV2rcVpcpc I2crppTr Iq2TrpV rrr I2pVccTqq IT2qqVr Ip2Tprcr Ir2pqrcr V I2qVVVT T I2qqpcr c Iq2ppcVT IV2crrrqrT p IVT2qrTVV q IV2rprVp r IVr2VppcT IT2pTVq ITc2pTTrqp IT2rrrqTpT V ITp2rqTVTqrT T Ic2cVqTT c IcT2rqTq 1(''(@&B IV2qqVTpcpc IV2qrTpVrV IV2qqTcr IV2cVVcqr IV2rqpcr I2qrcVpc I2VpT IV2rTTr I2cqTc I2ppVTrp I2crrcT I2rccqVVrp I2TTpqrqp I2Tcrpp I2qrrcc I2ccqc I2Tq I2VTVcVVpc 2VqcT 2pcTpqp 2Vpqcpq 2TcqqV 2rqr 2TVTr 2ppTTq 2TrTVV 2rVVppq 2pVpqVq 2cpVTVV 2rqpr 2Tpr 2cccVq 2pqVpcp 2cpcVcTq 2TVqqT 2VcpTVV 2VcVrp 2pcTcr 2rqrVq 2rTrTT 2VTrcqVc 2rVTcVTV 2Trr 2pqVTTpT 2TVrrpq 2TrTqV Projection Table AG2016 Appendix A 36 ׉ 7cassandra://X97HWfhZzTzJvofMRyO-IpBeltHnS4TZhN8fg-mtSzo!`j[ )C׉E 2cq cr V T c p q r p p p pV pT pc p pp pq pr q q q qV qT qc q qp qq qr r IT2TcTrcppp2rVrr I2TrVpp I2Vccp IT2VTqcp2rTTVrT I2cpVVpr I2pqrTc IT2prpprc2rcq I2pcT I2cpqp IT2prp2rqVT I2rpqrTq I2Tpcq IT2qpqrr2Trqp I2TcV I2pVV IV2rrTqV2pTprr I2qccrVpr IV2rTrcrT2TVrrp I2pqrTT IV2qcpVcqc2Trc I2TrqVpT IV2pVq2Tpp I2crqqVq IV2VrTc2qcrq I2Tqr IV2cVqpT2rcqq I2VVpcTVc IV2TTTqTrT2rc I2qrTqr IV2VTrTTpp2rppcqc I2pqqrrV IV2cpq2qcqpr I2qpVTVr IV2crTVcpT2qqcr I2pqVp IV2crcrq2pTTVq I2pcTV I2rqqVcpT2cpcr I2TpVTVpV I2qpVcpVc2Vpc I2VTcc I2ppprVpq2Tq I2qpVpTrq2rpTqqr I2cqTrcTrV2rTqVT I2Tqqr2rVrq I2VqTcrTVq2qqp I2qpTVqV2qrT 2cqVpqTT 2cTpqV 2qVqqc 2rVr 2ppq 2VVpp I2qqVpcr2prTqr I2qpTqT I2rprc2pcrpqc I2rTTq I2rrTVrVrc2pcpcV I2Tcq I2qrqcrpVp2rcVV I2qTr I2qTpTpp2pVrq I2qqV I2pqprcTq2cqTrr I2VqVrV I2pTc2cTrp I2pTcT I2cpTr2Trp I2TqpV I2TVVpqrq2TT I2qqVTp sFaHFW U V T c p q r V T c p q r V T c @UB Ic2rcVqTcr Ip2cpccqr Iq2ccpTr Iq2Vcrrp Iq2ccVcVq Iq2qTTcqp Iq2pTprcpr Iq2qccTrT Iq2qrrcTccc Iq2rTqVqr Iq2rpcVT Iq2rTcqVcT Iq2qppcVpV Iq2pqprcTcT Iq2prT Iq2TrpTqV Iq2rpVr Iq2rTcrT Ip2rVpqTTc Ip2rTrTT Ip2rVVcT Ip2rTcVTc Ip2rTqccTc Ip2rTVcVp Ip2rccr Ip2qrcT Ip2qTpqTVV !@UB 2VTTq 2rrcp 2crr 2VVrc 2crVVT 2rccc 2pqpqp 2TrVp 2qTprT 2ppqpppp 2TrVT 2crVcr 2TrT 2VrpTp 2VTprTp 2Vpcpp 2TrpT 2Vcqrp 2rTc 2VrTc 2cVT 2pTpV 2pVr 2Tr 2qVTc 2crc 2rrTTT ( '(@UB I2prpVT )&(@UB 2pqrqTpp 2Vp I2crrcVq 2crVT I2VTpcrc I2pprT I2VcpTp 2TTr 2qTqpr I2TTqrrrqV I2rqp I2qTp 2qTpr I2cTVVT I2VcTpT I2pVc I2pVc I2VcVqpV I2rqVpp 2pVq 2pT 2rqqrr I2VV I2rVqTpT I2VcT I2pcqq I2qpqVpc I2VTpVcT I2TVqrqVV I2Tqpqrq I2pTqTpp I2rqqqr I2TTVq I2cVrTV I2rcVVrT 2cqcTV 2qqTVr 2qpV 2pqVpcV 2TTTV 2qVcVpp 2qTrpT 2VVr 2Vrqcr 2TVqp 2prrcTp 2VTTqp 2pVqr 2V 2TcpqTpV 2Tqc 2qVTV 2ppc & rp rp rp rpV rpT rpc rp rpp rpq rpr rq rq rq rqV rqT rqc rq rqp rqq rqr rr rr rr rrV rrT rrc rr X@&B T2cTppqT T2pVprTrcr Vr2cppVpqV Vp2rcpTVVq Vc2cVTpq VT2rccT VV2qVqV p2Vcpqr p2Tqq T2rVcrrp 2qcpqV 2qcqp r2cTrpT q2VVrpqr V2pcT T2VcrVqp 2rrVcccT p2TpqrT c2qrrVrp c2pqccVr c2qcVcTp V2pTpcr 2pqqTp 2rTqT IV2cTcVrrV IV2qTqppr Ic2VcppVp 1(''(@&B Ic2TVTrr Ic2VVppcV IT2TprVVpr I2prcqrV Ip2qrqVT Ip2VcpT Ip2qcVrcV Iq2cccT Iq2cpTp Iq2qTcr Iq2rpcTr Ir2qTVc Iq2rqqcT Ir2qTV I2rr I2TqT IT2TpVpVp Ic2Vqqr IT2rrrqT I2qVVV IV2pqc I2Vpprq I2TTVT 2prpcVTpq 2TrT 2Tqpqp 2pqq 2TqVVT 2qqVrT 2cpqr 2Tpqccq 2TVVpp 2rqVTp 2ccVc 2rpc 2Vpqcq 2VTVqpT 2VqTqV 2Tcprcq 2TTqr 2TVVpc 2Tcppc 2Trcp 2cTrcT 2ccV 2cVVcr 2cVVVpqV 2cVpVVV 2cVVrqc 2TppVVVT 2TpTrpp 2TpprT 2TpVpTVrp 2TcrpTT 2TqVrT Projection Table AG2016 Appendix A 37 [ )Cȁ[ )Cǁ{בCט{u׉׉ 7cassandra://uhpE5EomfsTP1_CtWxChtRsFnvZe5Vhtk0ne1s9A8mAa` ׉ 7cassandra://IJCyoKfyzVX84pP4q9oiIORy0DefrwMcXJwVxroZBw4R`׉ 7cassandra://pFHnVPF-sTP1n9xfwEWw0Bj0eSQuLmtj7bWVLU5G1Bo\`j׉ 7cassandra://H4ZoQZLr2jA_NCwYCPZqBqdA_K3MtavGeXDVIG1yG7Aqd\͠ [ )C׉E p q r V V V VV VT Vc V Vp Vq Vr T T T TV TT Tc T Tp Tq Tr c c c cV cT cc c cp cq cr V T c p q r p p p pV pT pc p pp pq pr q q q qV qT qc q qp qq qr r Ip2qprr Ip2pcqVcqq Ip2rpccrc Ip2pqrTr Ip2cqVpTqq Ip2TqTrr Ip2TVc Ip2VrqqV Ip2qpr Ip2TTppr Ip2cqcpqVpV I2rTprVppc I2qqVVV I2ppVqVcqq I2ppqq I2cpqqqVV I2TpcVVVV I2VqVTqrqq I2qqTqqT I2rrcqr I2rTcrTp I2Vrp Ic2rTp Ic2qTrr Ic2pVqVTVr Ic2TqqVc Ic2cpVVTVTc Ic2Trppq Ic2TrVppc Ic2VrpcV Ic2TVpVVqp Ic2qrpp Ic2pcqTpTp IT2rqTrp IT2qrpTc IT2qpqTV IT2prpVp IT2Tprc IT2crTTV IT2TVcrTp IT2VVpq IT2VVpT IT2VqTTrV IT2VcT IV2rqVqcTT IV2qrTT IV2qrqpc IV2cpTVrqq IV2Tccqpc IV2VVTpqqq IV2rpTV IV2rqqVqq I2rpcc I2qTpqcc I2pVcp I2VqV I2TprVcrT I2VcqpTr I2TVTc I2Vrcrq I2qrTcp I2qrpVTcVTp I2pqqccc I2prT 2cp 2rqprTc 2rqTr 2VTT 2rqrT 2cpp 2rpqc 2rcrpp 2rcpcpr 2rpTrcc 2rTrVr 2rcqp 2rrT 2rVVprp 2qqTpcT 2qqrqcc 2qqrVpr 2qpqTrV 2qqp 2qTVTc 2qTpVq 2qcppqr 2qcccq 2qVqrrT 2qrqr 2qcVV 2qpqT 2qcVVq 2prrp 2qVqc 2qcVr 2qVprr 2qVpcTV 2qTpTqq 2qTqTqqq 2qqr 2rVVTp 2rVVcqr 2rc 2rrqTVV 2Vrrr 2Tqp 2Tpp 2Vpr 2qVV 2rVrT 2Trc 2cc 2pqT 2Tp 2Tq 2qcVr 2cprT 2cTVrc 2rqrVrT 2rcVT 2rpqq 2qqVTr 2qrT 2pqcrcq 2prV 2pqrp 2pcp 2cpcrV I2VVq I2VTVc I2qcTc I2 I2rpprT I2Tqrrrp I2qpTrr I2rTrVTr I2qTTT I2rrqc I2rpq I2cqpVV I2Vpqr I2qpVrr I2rpccrVr I2prpTVr I2pcrrrrp I2ppprqr I2rqpTp I2TVTVqq I2Trp I2VqrrTq I2TTT I2pcqq I2VqcV I2VVTqT I2cTcT I2TTr I2cp I2VpcqV I2Tqcqc I2TTpqqp I2TVTcpc I2TprT I2Vp I2cVTrTqVp I2Trcqcq I2TpVVTqq I2TppV I2Tppppp I2TrT I2VTVrVc I2Tqcppr I2TrTppcq I2VrVccq I2cVTr I2TprqrT I2TqVVr I2Tqqppr I2cTr I2VrqpVcT I2Tqrrq I2TVpcVq I2VrcrcVT I2Vqrqp I2VVpcq I2VcqT I2VVp I2rccVr I2r I2qTpp I2Tp I2rVVTc I2Vpc 2cr 2pVqVV 2pqq 2rqq 2cpqVccV 2VTcqq 2prT 2rp 2rq 2qpVppV 2TqTpcc 2qT 2rrqTq 2VVcr 2cVVrVT 2pqqrT 2cVqr 2cqcrcTp 2VTV 2cprqq 2qrpTp 2cprqT 2Tqc 2pqTp 2cVqc 2cprqT 2Vpc 2cqVV 2VcqV 2crV 2Tqrqcp 2prTqcp 2crrVT 2pTprpT 2pcpVrq 2prp 2cqcc 2ccVrc 2rVVT 2cq 2TVVc 2cVcq 2rTpTc 2cqpcpVp 2VTq 2Trcq 2cccV 2TTV 2TTppcp 2VpVqqcr 2VpqpTrr 2VTr 2qrTrTV 2rqpr 2crqV 2ccp 2Tqccp 2ppVqc 2VpT 2qc 2Tcrqc 2cp 2rpcTqpV 2cprr rrp rrq rrr V T c p q r V T c Iq2Tppqrq I2VqcprcpTp I2TVpqV IT2pcrVr Ip2TVrqpTp Ip2ppqV Iq2ccrqV Ic2VcVTT I2VVqprpp Ir2qqV IV2pTc IV2VcTVc IVT2qpcq IV2pc IT2cpTcqqp IVr2qqrTpTV IT2rrTqrccp ITc2prTpqcT ITp2qTrT V2VTcc T2TTpcc 2rTVT p2TrpTqT q2TpqTT q2rrTVV p2TVqcrVqp q2crrTVTr p2cVTTr q2rrq 2VcVcTqpT 2pVcqqTT c2Tppcp 2VcVrV p2pcccc p2ccpTVq 2pcVrr p2TTcTT 2rrrrp &&( ( I2pc 2rpVc Projection Table AG2016 Appendix A 38 ׉ 7cassandra://pFHnVPF-sTP1n9xfwEWw0Bj0eSQuLmtj7bWVLU5G1Bo\`j[ )C׉E'( &(( g 2VcTVq2pVVcTpT 2pVVcTpT2qTTqc 2VqTrT2qTqrp 7 2TqqV2r 2crrT I2VccTTV 2VprVT I2TcTqr2cVq 2pcprcVp2TpVrc 2rcVrqT '( &(( ' %( &( %( 2VqTrT I2cpTVpqp 2qTqrp2VccqqpTT 2rpqV I2TcTcTqr I2cpTVpqp2VccqqpTT I2TcTcTqr2pTrVV '( &(( ' %( &( %( ' %( &( %( Projection Table AG2016 Appendix A 39 [ )Cˁ[ )Cʁ{בCט{u׉׉ 7cassandra://w7ZWRvFI7ZQ7wqsE6BTToRCaovgF1YXn0S5uaSFiMBgs` ׉ 7cassandra://0AafaUxpLsUccxENky3RvmTV1aQaZJ325Bnin54O1Ow[`׉ 7cassandra://QFKTpUFTTe72FVwwQKDTojJtps7Lft4VQbJ2E-c5F34`j׉ 7cassandra://1rkfIg-WJ87hR7s-MeHqkX73GDg16BQ6uQo7FAjLkEIJv͠ [ )C׉E#APPENDIX B Model portfolio The model portfolios comprise no other forms of pension than a lifelong retirement pension and a lifelong survivor’s pension. There are six model portfolios which distinguish between young/average/old and male/female. Only multiples of 10 years are included as the ages of members, pensioners and surviving dependants. The average dataset is defined as the average between young and old. In the case of men, the rights resulting from male members (in other words, including widows) are included and in the case of women the rights resulting from female members (in other words, including widowers) are included. The weighted average age for the various categories is shown in table 15. Young Average Men Active and dormant Pensioners Survivors Women Active and dormant Pensioners Survivors 49.3 71.7 61.1 40.6 73.3 55.0 50.8 72.9 68.1 46.4 73.3 62.2 53.4 73.7 70.9 49.8 73.3 64.3 Table 15 Weighted average age of the model portfolios The distribution in numbers is shown in tables 16 and 17. Men (young) Men (average) 30 500 350 0 40 1200 840 0 50 2000 1400 150 60 1800 1260 150 70 1500 800 100 80 300 150 50 90 0 0 0 (65) (lat.) (i.p.) 300 210 0 Old Men (old) Age RP SP SP RP SP SP RP SP SP (65) (lat.) (i.p.) 850 595 0 1400 980 125 1800 1260 175 1650 950 250 550 275 175 50 25 50 500 350 0 800 560 100 1800 1260 200 1800 1100 400 800 400 300 100 50 100 Table 16 Numbers of members of the model portfolios comprising men ■ RP = retirement pension SP = survivor’s pension Projection Table AG2016 Appendix B 40 (65) (lat.) (i.p.) 100 70 0 ׉ 7cassandra://QFKTpUFTTe72FVwwQKDTojJtps7Lft4VQbJ2E-c5F34`j[ )C׉EWomen (young) Women (average) Women (old) Age RP SP SP RP SP SP RP SP SP (65) (lat.) (i.p.) 30 750 525 0 40 1000 700 0 50 500 350 50 60 200 140 50 70 100 50 0 80 50 20 0 (65) (lat.) (i.p.) 500 350 0 1000 700 0 1000 700 50 800 560 100 300 200 50 150 50 25 Table 17 Number of female members of the model portfolios ■ RP = retirement pension SP = survivor’s pension The technical provisions for these portfolios are calculated by applying the following assumptions: • the retirement age is 65; • the survivor’s pension is of the “unspecified partner” form up until the retirement date, after which it takes on the “specified partner” form; • the partner frequency is equal to 100% up to the retirement date; • the partner’s sex is not the same as that of the member; • within a civil partnership, the male is three years older than the female. (65) (lat.) (i.p.) 250 175 0 1000 700 0 1500 1050 50 1400 980 150 500 350 100 250 80 50 90 000 000 000 Projection Table AG2016 Appendix B 41 [ )C΁[ )Ć{בCט{u׉׉ 7cassandra://x-URzP786SWHudATla5JKVIYZB2C2ykH644EkjN7NiQC` ׉ 7cassandra://WV77JMTsVfbGzCEZGi7pSbOeC1RaorxHE5Zm8LMFvvUj`׉ 7cassandra://rtzmKTqLbZ2PsDZ5Epdy4Sx1hbX2bGx8VyNrEpnzyEo `j׉ 7cassandra://x07-pM1uaPK1vmcAmrlTXoUSchuxhRgNuENxPnNvsmIU2͠ [ )Cϕנ[ )C*E̬9ׁHhttp://www.mortality.org/ׁ ׁ Јנ[ )C*9ׁH+http://ec.europa.eu/eurostat/web/populationׁ ׁ Јנ[ )C*9ׁH+http://ec.europa.eu/eurostat/web/populationׁ ׁ Јנ[ )C*= 9ׁHFhttp://statline.cbs.nl/Statweb/publication/?DM=SLNL&PA=37168&D1=a&D2=1ׁ ׁ Јנ[ )C* 9ׁHHhttp://statline.cbs.nl/Statweb/publication/?DM=SLNL&PA=7461BEV&D1=0&D2=1ׁ ׁ Ј׉EwAPPENDIX C Literature and data used This report assumes the data available on 20 April 2016 (Eurostat), 29 April 2016 (Statline Exposures), 12 May 2016 (Statline Observed Deaths) and 13 June 2016 (for the HMD data). [1] CBS data from Statline up to and including 2015. Exposures-to-Risk; version of 29 April 2016. This version is the same as the version of 20 June 2016 for the ages from 0 up to and including 90 years: http://statline.cbs.nl/Statweb/publication/?DM=SLNL&PA=7461BEV&D1=0&D2=12&D3=1-133&D4=65-66&VW=T Observed Deaths; version of 12 May 2016: http://statline.cbs.nl/Statweb/publication/?DM=SLNL&PA=37168&D1=a&D2=12&D3=0%2c56-162&D4=0&D5=60-64&HDR=G3%2cT%2cG1&STB=G2%2cG4&VW=T [2] Eurostat data; version of March 2016. Exposures to Risk (demo_pjan): http://ec.europa.eu/eurostat/web/population-demography-migrationprojections/population-data/database Observed Deaths (demo_mager en demo_magec): http://ec.europa.eu/eurostat/web/population-demography-migrationprojections/deaths-life-expectancy-data/database [3] HMD-database: http://www.mortality.org/ [4] V. Kannisto. Development of the oldest – old mortality, 1950-1980: evidence form 28 developed countries. Odense University Press, 1992. [5] N. Li and R Lee. Coherent Mortality Forecasts for a Group of Populations: An Extension of the Lee-Carter Method. Demography 42(3), pp. 575-594, 2005 Projection Table AG2016 Appendix C 42 ׉ 7cassandra://rtzmKTqLbZ2PsDZ5Epdy4Sx1hbX2bGx8VyNrEpnzyEo `j[ )C׉EGAPPENDIX D Glossary State Pension age (AOW) The age at which a person is eligible for a state old-age pension (AOW). In years 2014 up to the including 2021, this age will be increased gradually from 65 years to 67 years. Further increases after this date depend on the future development of (estimated) life expectancy. Best estimate In this publication: the most probable value of a quantity subject to coincidence, such as a mortality probability, the value of a product or portfolio et cetera. CMI model. RMS model. Life Metrics projection models Classes of stochastic models Cohort life expectancy Life expectancy based on a projection life table. This means that the life expectancy of an individual is based on mortality probabilities from the mortality table corresponding to the observation year in which the respective individual has a certain age. Deterministic projection life table A projection table in which the mortality figures for future years are determined on the basis of a model in which uncertainties are not taken into account. As a result, there is 1 (deterministic) outcome. Eurostat database The Eurostat database (Eurostat is the statistics office of the European Union) offers a wide range of data which can be used by governments, companies, the education sector, journalists and the general public. Human Mortality Database (HMD) An international database with population and mortality data from more than 35 countries worldwide. Survivor’s pension in payment A form of insurance in which the surviving dependent (the co-insured) of the principal insured receives a periodic benefit after the principal insured has died. Kannistö closure of the table A method of determining mortality probabilities at high ages through extrapolation from mortality probabilities at lower ages. Latent survivor’s pension Type of insurance—linked to the retirement pension—whereby a provision is accumulated from which a benefit can be paid periodically to the surviving dependant for the remainder of his or her life after the death of the principal insured. Projection Table AG2016 Appendix D 43 [ )Cс[ )CЁ{בCט{u׉׉ 7cassandra://ogbzSeEvN7-H4FggwEQhpvmQuhc0utZ_XZf-yqTdZp0 ` ׉ 7cassandra://9bp-S3G7gjHrlzSSle61jTgMFoXm78xSdY-iNAy7CYY;`׉ 7cassandra://4tyTI5AM--_IFeOG_wxP7t-FZ22oOkv0cbNMHKVgMr0`j׉ 7cassandra://e8SnjpukplKUKpMt5EPbj4PhqgbFnD-FhZA5OKPmKzo): ͠ [ )C׉ELife expectancy In most publications, the concept of life expectancy refers to the expected (remaining) life of a person at birth. The publication. Projection Table AG2014, refers to remaining life expectancy because this concept applies to every age. This may relate to period life expectancy or cohort life expectancy. Retirement pension A type of insurance in which the insured member (the principle insured) receives a periodic benefit after attaining the retirement age and for as long as he or she is alive. Period life expectancy Life expectancy based on a period table. Period table A mortality table based on observed mortality figures from one or more observation years. The Association uses the mortality figures of five preceding calendar years for its period tables. A period table does not take into account the developments of mortality and, in doing so, assumes constant mortality probabilities for future years. Projection period The number of future years in which conclusions are stated about mortality figures in accordance with the model. projection life table A mortality table in which mortality figures are stated for each future year. As a result, mortality probabilities are available for each combination of age and observation year. It is therefore possible to calculate a remaining life expectancy for each age and for every (future) year. Statline Statline is the public databank of Statistics Netherlands and provides figures on the economy, the population of the Netherlands and our society. Stochastic model A model in which the future mortality probabilities are not specified but are described by means of probability distributions. Stochastic projection life table A projection table which is the outcome of the use of a stochastic model and which therefore assumes various values for various scenarios of the coincidence variables (as can be observed in simulations). Projection Table AG2016 Appendix D 44 ׉ 7cassandra://4tyTI5AM--_IFeOG_wxP7t-FZ22oOkv0cbNMHKVgMr0`j[ )C׈E[ )Cԁ[ )CӁ{בCט{u׉׉ 7cassandra://n3Py-kh5-mGzJUUuTyoM83qBwAcXDh8qgsldDLvIG-s͏` ׉ 7cassandra://j9V5f7WAVl_euzLEpUcTtQuD12gYB3z3OIwy0ozIrEg`S׉ 7cassandra://GbHjFZH8CfEvLObYFSxiNcCungBzxzTVuCL5hb6aBk8`̵׉ 7cassandra://T7lE-pfDTVZevWQPJYTnPsiTicQxOazXuR-Dpe4KbkQ$S͠[ )CՑנ[ )C]9ׁHhttp://www.ag-ai.nlׁ ׁ Ј׉E7Colophon Publication Royal Dutch Actuarial Association, Groenewoudsedijk 80, 3528 BK Utrecht telephone: 31-(0)30-686 61 50, website: www.ag-ai.nl Design Stahl Ontwerp, Nijmegen Print Selection Print & Mail, Woerden Vertaling Robert Ensor, Professional Language Services BV, Amsterdam Projection Table AG2016 46 ׉ 7cassandra://GbHjFZH8CfEvLObYFSxiNcCungBzxzTVuCL5hb6aBk8`̵[ )C׈E[ )Cׁ[ )Cց{)Projection table AG2016qProjection table AG2016 of the Royal Dutch Actuarial Association (Koninklijk Actuarieel Genootschap or ‘AG’).[ {a;