Actuarial mathematics for life contingent risks:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Pr.
2013
|
| Edition: | 2. ed. |
| Series: | International series on actuarial science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references |
| Physical Description: | XXI, 597 S. graph. Darst. |
| ISBN: | 9781107044074 |
Staff View
MARC
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| 245 | 1 | 0 | |a Actuarial mathematics for life contingent risks |c David C.M. Dickson ; Mary R. Hardy ; Howard R. Waters |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Pr. |c 2013 | |
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Record in the Search Index
| _version_ | 1804151542703456256 |
|---|---|
| adam_text | Titel: Actuarial mathematics for life contingent risks
Autor: Dickson, David C. M
Jahr: 2013
Contents
Preface to the second edition page xvii
1 Introduction to life insurance 1
1.1 Summary 1
1.2 Background 1
1.3 Life insurance and annuity contracts 3
1.3.1 Introduction 3
1.3.2 Traditional insurance contracts 4
1.3.3 Modern insurance contracts 6
1.3.4 Distribution methods 7
1.3.5 Underwriting 8
1.3.6 Premiums 10
1.3.7 Life annuities 11
1.4 Other insurance contracts 12
1.5 Pension benefits 12
1.5.1 Defined benefit and defined contribution 12
1.5.2 Defined benefit pension design 13
1.6 Mutual and proprietary insurers 13
1.7 Typical problems 14
1.8 Notes and further reading 15
1.9 Exercises 15
2 Survival models 17
2.1 Summary 17
2.2 The future lifetime random variable 17
2.3 The force of mortality 21
2.4 Actuarial notation 26
2.5 Mean and standard deviation of Tx 28
2.6 Curtate future lifetime 32
2.6.1 Kx andex 32
2.6.2 The complete and curtate expected future
lifetimes, ex and ex 34
2.7 Notes and further reading 34
2.8 Exercises 36
3 Life tables and selection 41
3.1 Summary 41
3.2 Life tables 41
3.3 Fractional age assumptions 44
3.3.1 Uniform distribution of deaths 44
3.3.2 Constant force of mortality 48
3.4 National life tables 49
3.5 Survival models for life insurance policyholders 52
3.6 Life insurance underwriting 54
3.7 Select and ultimate survival models 55
3.8 Notation and formulae for select survival models 58
3.9 Select life tables 59
3.10 Some comments on heterogeneity in mortality 65
3.11 Mortality trends 67
3.12 Notes and further reading 69
3.13 Exercises 70
4 Insurance benefits 76
4.1 Summary 76
4.2 Introduction 76
4.3 Assumptions 77
4.4 Valuation of insurance benefits 78
4.4.1 Whole life insurance: the continuous case, Äx 78
4.4.2 Whole life insurance: the annual case, Ax 81
4.4.3 Whole life insurance: the 1 /mthly case, Axm 82
4.4.4 Recursions 84
4.4.5 Term insurance 88
4.4.6 Pure endowment 90
4.4.7 Endowment insurance 90
4.4.8 Deferred insurance benefits 93
4.5 Relating Äx, Ax and A*m) 94
4.5.1 Using the uniform distribution of deaths
assumption 95
4.5.2 Using the claims acceleration approach 96
4.6 Variable insurance benefits 98
4.7 Functions for select lives 102
4.8 Notes and further reading 103
4.9 Exercises 103
5 Annuities 109
5.1 Summary 109
5.2 Introduction 109
5.3 Review of annuities-certain 110
5.4 Annual life annuities 110
5.4.1 Whole life annuity-due 111
5.4.2 Term annuity-due 113
5.4.3 Whole life immediate annuity 115
5.4.4 Term immediate annuity 115
5.5 Annuities payable continuously 116
5.5.1 Whole life continuous annuity 116
5.5.2 Term continuous annuity 118
5.6 Annuities payable 1 /mthly 119
5.6.1 Introduction 119
5.6.2 Whole life annuities payable 1/rathly 120
5.6.3 Term annuities payable 1/mthly 121
5.7 Comparison of annuities by payment frequency 122
5.8 Deferred annuities 124
5.9 Guaranteed annuities 127
5.10 Increasing annuities 128
5.10.1 Arithmetically increasing annuities 129
5.10.2 Geometrically increasing annuities 130
5.11 Evaluating annuity functions 131
5.11.1 Recursions 131
5.11.2 Applying the UDD assumption 132
5.11.3 Woolhouse s formula 133
5.12 Numerical illustrations 136
5.13 Functions for select lives 137
5.14 Notes and further reading 138
5.15 Exercises 138
6 Premium calculation 144
6.1 Summary 144
6.2 Preliminaries 144
6.3 Assumptions 146
6.4 The present value of future loss random variable 146
6.5 The equivalence principle 147
6.5.1 Net premiums 147
6.6 Gross premiums 151
6.7 Profit 157
6.8 The portfolio percentile premium principle 163
6.9 Extra risks 167
6.9.1 Age rating 167
6.9.2 Constant addition to fj,x 167
6.9.3 Constant multiple of mortality rates 169
6.10 Notes and further reading 170
6.11 Exercises 171
7 Policy values 178
7.1 Summary 178
7.2 Assumptions 179
7.3 Policies with annual cash flows 179
7.3.1 The future loss random variable 179
7.3.2 Policy values for policies with annual cash flows 185
7.3.3 Recursive formulae for policy values 192
7.3.4 Annual profit by source 198
7.3.5 Asset shares 202
7.4 Policy values for policies with cash flows at 1/mthly
intervals 205
7.4.1 Recursions 206
7.4.2 Valuation between premium dates 207
7.5 Policy values with continuous cash flows 209
7.5.1 Thiele s differential equation 209
7.5.2 Numerical solution of Thiele s differential
equation 212
7.6 Policy alterations 215
7.7 Retrospective policy values 220
7.7.1 Prospective and retrospective valuation 220
7.7.2 Defining the retrospective net premium policy
value 222
7.8 Negative policy values 225
7.9 Deferred acquisition expenses and modified premium
reserves 226
7.10 Notes and further reading 231
7.11 Exercises 231
8 Multiple state models 242
8.1 Summary 242
8.2 Examples of multiple state models 242
8.2.1 The alive-dead model 243
8.2.2 Term insurance with increased benefit on
accidental death 244
8.2.3 The permanent disability model 245
8.2.4 The disability income insurance model 245
8.3 Assumptions and notation 246
8.4 Formulae for probabilities 250
8.4.1 Kolmogorov s forward equations 254
8.5 Numerical evaluation of probabilities 254
8.6 Premiums 258
8.7 Policy values and Thiele s differential equation 261
8.7.1 The disability income insurance model 262
8.7.2 Thiele s differential equation - the general case 266
8.8 Multiple decrement models 267
8.9 Multiple decrement tables 271
8.9.1 Fractional age assumptions for decrements 273
8.10 Constructing a multiple decrement table 275
8.10.1 Deriving independent rates from dependent rates 275
8.10.2 Deriving dependent rates from independent rates 277
8.11 Comments on multiple decrement notation 279
8.12 Transitions at exact ages 279
8.13 Markov multiple state models in discrete time 284
8.13.1 The Chapman-Kolmogorov equations 288
8.13.2 Transition matrices 289
8.14 Notes and further reading 291
8.15 Exercises 292
9 Joint life and last survivor benefits 303
9.1 Summary 303
9.2 Joint life and last survivor benefits 303
9.3 Joint life notation 304
9.4 Independent future lifetimes 308
9.5 A multiple state model for independent future
lifetimes 314
9.6 A model with dependent future lifetimes 319
9.7 The common shock model 325
9.8 Notes and further reading 328
9.9 Exercises 328
10 Pension mathematics 334
10.1 Summary 334
10.2 Introduction 334
10.3 The salary scale function 335
10.4 Setting the DC contribution 339
10.5 The service table 342
10.6 Valuation of benefits 351
10.6.1 Final salary plans 351
10.6.2 Career average earnings plans 357
10.7 Funding the benefits 358
10.8 Notes and further reading 363
10.9 Exercises 364
11 Yield curves and non-diversifiable risk 371
11.1 Summary 371
11.2 The yield curve 371
11.3 Valuation of insurances and life annuities 375
11.3.1 Replicating the cash flows of a traditional
non-participating product 377
11.4 Diversifiable and non-diversifiable risk 378
11.4.1 Diversifiable mortality risk 379
11.4.2 Non-diversifiable risk 380
11.5 Monte Carlo simulation 386
11.6 Notes and further reading 391
11.7 Exercises 392
12 Emerging costs for traditional life insurance 397
12.1 Summary 397
12.2 Introduction 397
12.3 Profit testing a term insurance policy 399
12.3.1 Time step 399
12.3.2 Profit test basis 399
12.3.3 Incorporating reserves 403
12.3.4 Profit signature 406
12.4 Profit testing principles 407
12.4.1 Assumptions 407
12.4.2 The profit vector 407
12.4.3 The profit signature 408
12.4.4 The net present value 409
12.4.5 Notes on the profit testing method 409
12.5 Profit measures 410
12.6 Using the profit test to calculate the premium 412
12.7 Using the profit test to calculate reserves 413
12.8 Profit testing for multiple state models 415
12.9 Notes 422
12.10 Exercises 423
13 Participating and Universal Life insurance 431
13.1 Summary 431
13.2 Introduction 431
13.3 Participating insurance 434
13.3.1 Introduction 434
13.3.2 Examples 435
13.3.3 Notes on profit distribution methods 443
13.4 Universal Life insurance 444
13.4.1 Introduction 444
13.4.2 Key design features 445
13.4.3 Projecting account values 447
13.4.4 Profit testing Universal Life policies 448
13.4.5 Universal Life Type B 449
13.4.6 Universal Life Type A 455
13.4.7 No-lapse guarantees 462
13.4.8 Comments on UL profit testing 463
13.5 Comparison of UL and whole life insurance policies 464
13.6 Notes and further reading 464
13.7 Exercises 465
14 Emerging costs for equity-linked insurance 473
14.1 Summary 473
14.2 Equity-linked insurance 473
14.3 Deterministic profit testing for equity-linked insurance 475
14.4 Stochastic profit testing 486
14.5 Stochastic pricing 490
14.6 Stochastic reserving 492
14.6.1 Reserving for policies with non-diversifiable risk 492
14.6.2 Quantité reserving 493
14.6.3 CTE reserving 495
14.6.4 Comments on reserving 496
14.7 Notes and further reading 497
14.8 Exercises 497
15 Option pricing 503
15.1 Summary 503
15.2 Introduction 503
15.3 The no-arbitrage assumption 504
15.4 Options 505
15.5 The binomial option pricing model 507
15.5.1 Assumptions 507
15.5.2 Pricing over a single time period 507
15.5.3 Pricing over two time periods 512
15.5.4 Summary of the binomial model option pricing
technique 515
15.6 The Black-Scholes-Merton model 515
15.6.1 The model 515
15.6.2 The Black-Scholes-Merton option pricing
formula 517
15.7 Notes and further reading 529
15.8 Exercises 529
16 Embedded options 532
16.1 Summary 532
16.2 Introduction 532
16.3 Guaranteed minimum maturity benefit 534
16.3.1 Pricing 534
16.3.2 Reserving 537
16.4 Guaranteed minimum death benefit 539
16.4.1 Pricing 539
16.4.2 Reserving 541
16.5 Pricing methods for embedded options 545
16.6 Risk management 548
16.7 Emerging costs 550
16.8 Notes and further reading 558
16.9 Exercises 559
A Probability theory 564
A.l Probability distributions 564
A. 1.1 Binomial distribution 564
A. 1.2 Uniform distribution 564
A. 1.3 Normal distribution 565
A. 1.4 Lognormal distribution 566
A.2 The central limit theorem 568
A.3 Functions of a random variable 569
A.3.1 Discrete random variables 569
A.3.2 Continuous random variables 570
A.3.3 Mixed random variables 571
A.4 Conditional expectation and conditional variance 572
A.5 Notes and further reading 573
B Numerical techniques 574
B.l Numerical integration 574
B.l.l The trapezium rule 574
B.l.2 Repeated Simpson s rule 575
B. 1.3 Integrals over an infinite interval 576
B.2 Woolhouse s formula 577
B.3 Notes and further reading 578
C Simulation 579
C.l The inverse transform method 579
C.2 Simulation from a normal distribution 580
C.2.1 The Box-Muller method 580
C.2.2 The polar method 581
C.3 Notes and further reading 581
D Tables 582
References 589
Index 592
|
| any_adam_object | 1 |
| author | Dickson, David C. M. 1959- |
| author_GND | (DE-588)170828891 (DE-588)170950379 |
| author_facet | Dickson, David C. M. 1959- |
| author_role | aut |
| author_sort | Dickson, David C. M. 1959- |
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| building | Verbundindex |
| bvnumber | BV041424077 |
| callnumber-first | H - Social Science |
| callnumber-label | HG8781 |
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| callnumber-search | HG8781 |
| callnumber-sort | HG 48781 |
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| dewey-ones | 368 - Insurance |
| dewey-raw | 368/.01 |
| dewey-search | 368/.01 |
| dewey-sort | 3368 11 |
| dewey-tens | 360 - Social problems and services; associations |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV041424077 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:56:29Z |
| institution | BVB |
| isbn | 9781107044074 |
| language | English |
| lccn | 2013013708 |
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| owner | DE-N2 DE-20 |
| owner_facet | DE-N2 DE-20 |
| physical | XXI, 597 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series2 | International series on actuarial science |
| spelling | Dickson, David C. M. 1959- Verfasser (DE-588)170828891 aut Actuarial mathematics for life contingent risks David C.M. Dickson ; Mary R. Hardy ; Howard R. Waters 2. ed. Cambridge [u.a.] Cambridge Univ. Pr. 2013 XXI, 597 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series on actuarial science Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references Mathematik Insurance Mathematics Risk (Insurance) Mathematics Lebensversicherung (DE-588)4034928-7 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Risiko (DE-588)4050129-2 gnd rswk-swf Lebensversicherung (DE-588)4034928-7 s Risiko (DE-588)4050129-2 s Versicherungsmathematik (DE-588)4063194-1 s 1\p DE-604 Hardy, Mary Anderson Sonstige oth Waters, Howard R. Sonstige (DE-588)170950379 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026871080&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dickson, David C. M. 1959- Actuarial mathematics for life contingent risks Mathematik Insurance Mathematics Risk (Insurance) Mathematics Lebensversicherung (DE-588)4034928-7 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Risiko (DE-588)4050129-2 gnd |
| subject_GND | (DE-588)4034928-7 (DE-588)4063194-1 (DE-588)4050129-2 |
| title | Actuarial mathematics for life contingent risks |
| title_auth | Actuarial mathematics for life contingent risks |
| title_exact_search | Actuarial mathematics for life contingent risks |
| title_full | Actuarial mathematics for life contingent risks David C.M. Dickson ; Mary R. Hardy ; Howard R. Waters |
| title_fullStr | Actuarial mathematics for life contingent risks David C.M. Dickson ; Mary R. Hardy ; Howard R. Waters |
| title_full_unstemmed | Actuarial mathematics for life contingent risks David C.M. Dickson ; Mary R. Hardy ; Howard R. Waters |
| title_short | Actuarial mathematics for life contingent risks |
| title_sort | actuarial mathematics for life contingent risks |
| topic | Mathematik Insurance Mathematics Risk (Insurance) Mathematics Lebensversicherung (DE-588)4034928-7 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Risiko (DE-588)4050129-2 gnd |
| topic_facet | Mathematik Insurance Mathematics Risk (Insurance) Mathematics Lebensversicherung Versicherungsmathematik Risiko |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026871080&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dicksondavidcm actuarialmathematicsforlifecontingentrisks AT hardymaryanderson actuarialmathematicsforlifecontingentrisks AT watershowardr actuarialmathematicsforlifecontingentrisks |