Modelling longevity dynamics for pensions and annuity business:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford University Press
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. [373]-387) and index |
| Beschreibung: | xix, 395 S. graph. Darst. 24 cm |
| ISBN: | 9780199547272 0199547270 |
Internformat
MARC
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| 245 | 1 | 0 | |a Modelling longevity dynamics for pensions and annuity business |c Ermanno Pitacco ... [et al.] |
| 246 | 1 | 3 | |a Modeling longevity dynamics for pensions and annuity business |
| 264 | 1 | |a Oxford [u.a.] |b Oxford University Press |c 2009 | |
| 300 | |a xix, 395 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. [373]-387) and index | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Life insurance |x Mathematics | |
| 650 | 4 | |a Mortality |v Tables | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
1 Life annuities 1
1.1 Introduction 1
1.2 Annuities-certain versus life annuities 2
1.2.1 Withdrawing from a fund 2
1.2.2 Avoiding early fund exhaustion 5
1.2.3 Risks in annuities-certain and in life annuities 6
1.3 Evaluating life annuities: deterministic approach 8
1.3.1 The life annuity as a financial transaction 8
1.3.2 Actuarial values 9
1.3.3 Technical bases 12
1.4 Cross-subsidy in life annuities 14
1.4.1 Mutuality 14
1.4.2 Solidarity 16
1.4.3 Tontine annuities 18
1.5 Evaluating life annuities: stochastic approach 20
1.5.1 The random present value of a life annuity 20
1.5.2 Focussing on portfolio results 21
1.5.3 A first insight into risk and solvency 24
1.5.4 Allowing for uncertainty in mortality
assumptions 27
1.6 Types of life annuities 31
1.6.1 Immediate annuities versus deferred annuities 31
1.6.2 The accumulation period 33
1.6.3 The decumulation period 36
1.6.4 The payment profile 38
1.6.5 About annuity rates 40
1.6.6 Variable annuities and GMxB features 41
1.7 References and suggestions for further reading 43
Contents
2 The basic mortality model 45
2.1 Introduction 45
2.2 Life tables 46
2.2.1 Cohort tables and period tables 46
2.2.2 Population tables versus market tables 47
2.2.3 The life table as a probabilistic model 48
2.2.4 Select mortality 49
2.3 Moving to an age-continuous context 51
2.3.1 The survival function 51
2.3.2 Other related functions 53
2.3.3 The force of mortality 55
2.3.4 The central death rate 57
2.3.5 Assumptions for non-integer ages 57
2.4 Summarizing the lifetime probability distribution 58
2.4.1 The life expectancy 59
2.4.2 Other markers 60
2.4.3 Markers under a dynamic perspective 62
2.5 Mortality laws 63
2.5.1 Laws for the force of mortality 64
2.5.2 Laws for the annual probability of death 66
2.5.3 Mortality by causes 67
2.6 Non-parametric graduation 67
2.6.1 Some preliminary ideas 67
2.6.2 The Whittaker-Henderson model 68
2.6.3 Splines 69
2.7 Some transforms of the survival function 73
2.8 Mortality at very old ages 74
2.8.1 Some preliminary ideas 74
2.8.2 Models for mortality at highest ages 75
2.9 Heterogeneity in mortality models 77
2.9.1 Observable heterogeneity factors 77
2.9.2 Models for differential mortality 78
2.9.3 Unobservable heterogeneity factors.
The frailty 80
2.9.4 Frailty models 83
2.9.5 Combining mortality laws with frailty models 85
2.10 References and suggestions for further reading 87
Contents
Mortality trends during the 20th century 89
3.1 Introduction 89
3.2 Data sources 90
3.2.1 Statistics Belgium 91
3.2.2 Federal Planning Bureau 91
3.2.3 Human mortality database 92
3.2.4 Banking, Finance, and Insurance Commission 92
3.3 Mortality trends in the general population 93
3.3.1 Age-period life tables 93
3.3.2 Exposure-to-risk 95
3.3.3 Death rates 96
3.3.4 Mortality surfaces 101
3.3.5 Closure of life tables 101
3.3.6 Rectangularization and expansion 105
3.3.7 Life expectancies 111
3.3.8 Variability 113
3.3.9 Heterogeneity 115
3.4 Life insurance market 116
3.4.1 Observed death rates 116
3.4.2 Smoothed death rates 118
3.4.3 Life expectancies 122
3.4.4 Relational models 123
3.4.5 Age shifts 127
3.5 Mortality trends throughout EU 129
3.6 Conclusions 135
4 Forecasting mortality: an introduction 137
4.1 Introduction 137
4.2 A dynamic approach to mortality modelling 139
4.2.1 Representing mortality dynamics: single-figures
versus age-specific functions 139
4.2.2 A discrete, age-specific setting 140
4.3 Projection by extrapolation of annual probabilities
of death 141
4.3.1 Some preliminary ideas 141
4.3.2 Reduction factors 144
Contents
4.3.3 The exponential formula 145
4.3.4 An alternative approach to the exponential
extrapolation 146
4.3.5 Generalizing the exponential formula 147
4.3.6 Implementing the exponential formula 148
4.3.7 A general exponential formula 149
4.3.8 Some exponential formulae used in
actuarial practice 149
4.3.9 Other projection formulae 151
4.4 Using a projected table 152
4.4.1 The cohort tables in a projected table 152
4.4.2 From a double-entry to a single-entry
projected table 153
4.4.3 Age shifting 155
4.5 Projecting mortality in a parametric context 156
4.5.1 Mortality laws and projections 156
4.5.2 Expressing mortality trends
via Weibull s parameters 160
4.5.3 Some remarks 162
4.5.4 Mortality graduation over age and time 163
4.6 Other approaches to mortality projections 165
4.6.1 Interpolation versus extrapolation:
the limit table 165
4.6.2 Model tables 166
4.6.3 Projecting transforms of life table functions 167
4.7 The Lee-Carter method: an introduction 169
4.7.1 Some preliminary ideas 169
4.7.2 The LC model 171
4.7.3 From LC to the Poisson log-bilinear model 172
4.7.4 The LC method and model tables 173
4.8 Further issues 173
4.8.1 Cohort approach versus period approach.
APC models 173
4.8.2 Projections and scenarios. Mortality
by causes 175
4.9 References and suggestions for further reading 175
4.9.1 Landmarks in mortality projections 175
4.9.2 Further references 178
Contents
5 Forecasting mortality: applications and examples
of age-period models 181
5.1 Introduction 181
5.2 Lee-Carter mortality projection model 186
5.2.1 Specification 186
5.2.2 Calibration 188
5.2.3 Application to Belgian mortality statistics 200
5.3 Cairns-Blake-Dowd mortality projection model 203
5.3.1 Specification 203
5.3.2 Calibration 206
5.3.3 Application to Belgian mortality statistics 207
5.4 Smoothing 209
5.4.1 Motivation 209
5.4.2 P-splines approach 210
5.4.3 Smoothing in the Lee-Carter model 212
5.4.4 Application to Belgian mortality statistics 213
5.5 Selection of an optimal calibration period 214
5.5.1 Motivation 214
5.5.2 Selection procedure 216
5.5.3 Application to Belgian mortality statistics 217
5.6 Analysis of residuals 218
5.6.1 Deviance and Pearson residuals 218
5.6.2 Application to Belgian mortality statistics 220
5.7 Mortality projection 221
5.7.1 Time series modelling for the time indices 221
5.7.2 Modelling of the Lee-Carter time index 223
5.7.3 Modelling the Cairns-Blake-Dowd time indices 228
5.8 Prediction intervals 229
5.8.1 Why bootstrapping? 229
5.8.2 Bootstrap percentiles confidence intervals 230
5.8.3 Application to Belgian mortality statistics 232
5.9 Forecasting life expectancies 234
5.9.1 Official projections performed by the Belgian
Federal Planning Bureau (FPB) 235
5.9.2 Andreev-Vaupel projections 235
5.9.3 Application to Belgian mortality statistics 237
Contents
5.9.4 Longevity fan charts 240
5.9.5 Back testing 240
6 Forecasting mortality: applications and examples of
age-period-cohort models 243
6.1 Introduction 243
6.2 LC age-period-cohort mortality projection model 246
6.2.1 Model structure 246
6.2.2 Error structure and model fitting 248
6.2.3 Mortality rate projections 253
6.2.4 Discussion 253
6.3 Application to United Kingdom mortality data 254
6.4 Cairns-Blake-Dowd mortality projection model:
allowing for cohort effects 263
6.5 P-splines model: allowing for cohort effects 265
7 The longevity risk: actuarial perspectives 267
7.1 Introduction 267
7.2 The longevity risk 268
7.2.1 Mortality risks 268
7.2.2 Representing longevity risk: stochastic
modelling issues 270
7.2.3 Representing longevity risk: some examples 273
7.2.4 Measuring longevity risk in a static framework 276
7.3 Managing the longevity risk 293
7.3.1 A risk management perspective 293
7.3.2 Natural hedging 299
7.3.3 Solvency issues 303
7.3.4 Reinsurance arrangements 318
7.4 Alternative risk transfers 330
7.4.1 Life insurance securitization 330
7.4.2 Mortality-linked securities 332
7.4.3 Hedging life annuity liabilities through
longevity bonds 337
7.5 Life annuities and longevity risk 343
7.5.1 The location of mortality risks in traditional
life annuity products 343
7.5.2 GAOandGAR 346
7.5.3 Adding flexibility to GAR products 347
Contents
7.6 Allowing for longevity risk in pricing 350
7.7 Financing post-retirement income 354
7.7.1 Comparing life annuity prices 354
7.7.2 Life annuities versus income drawdown 356
7.7.3 The mortality drag 359
7.7.4 Flexibility in financing post-retirement income 363
7.8 References and suggestions for further reading 369
References 373
Index 389
|
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| author | Pitacco, Ermanno 1947-2022 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV040398559 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:23:10Z |
| institution | BVB |
| isbn | 9780199547272 0199547270 |
| language | English |
| lccn | 2009417720 |
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| publisher | Oxford University Press |
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| spelling | Pitacco, Ermanno 1947-2022 Verfasser (DE-588)138165246 aut Modelling longevity dynamics for pensions and annuity business Ermanno Pitacco ... [et al.] Modeling longevity dynamics for pensions and annuity business Oxford [u.a.] Oxford University Press 2009 xix, 395 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. [373]-387) and index Mathematik Life insurance Mathematics Mortality Tables Sterblichkeit (DE-588)4057312-6 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Lebensversicherung (DE-588)4034928-7 gnd rswk-swf Lebensversicherung (DE-588)4034928-7 s Sterblichkeit (DE-588)4057312-6 s Versicherungsmathematik (DE-588)4063194-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025251791&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pitacco, Ermanno 1947-2022 Modelling longevity dynamics for pensions and annuity business Mathematik Life insurance Mathematics Mortality Tables Sterblichkeit (DE-588)4057312-6 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Lebensversicherung (DE-588)4034928-7 gnd |
| subject_GND | (DE-588)4057312-6 (DE-588)4063194-1 (DE-588)4034928-7 |
| title | Modelling longevity dynamics for pensions and annuity business |
| title_alt | Modeling longevity dynamics for pensions and annuity business |
| title_auth | Modelling longevity dynamics for pensions and annuity business |
| title_exact_search | Modelling longevity dynamics for pensions and annuity business |
| title_full | Modelling longevity dynamics for pensions and annuity business Ermanno Pitacco ... [et al.] |
| title_fullStr | Modelling longevity dynamics for pensions and annuity business Ermanno Pitacco ... [et al.] |
| title_full_unstemmed | Modelling longevity dynamics for pensions and annuity business Ermanno Pitacco ... [et al.] |
| title_short | Modelling longevity dynamics for pensions and annuity business |
| title_sort | modelling longevity dynamics for pensions and annuity business |
| topic | Mathematik Life insurance Mathematics Mortality Tables Sterblichkeit (DE-588)4057312-6 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Lebensversicherung (DE-588)4034928-7 gnd |
| topic_facet | Mathematik Life insurance Mathematics Mortality Tables Sterblichkeit Versicherungsmathematik Lebensversicherung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025251791&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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