Practical risk theory for actuaries:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall
1994
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Monographs on statistics and applied probability
53 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 546 S. graph. Darst. |
| ISBN: | 0412428504 |
Internformat
MARC
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| 100 | 1 | |a Daykin, Christopher D. |e Verfasser |0 (DE-588)170517632 |4 aut | |
| 245 | 1 | 0 | |a Practical risk theory for actuaries |c C. D. Daykin, T. Pentikäinen and M. Pesonen |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London [u.a.] |b Chapman & Hall |c 1994 | |
| 300 | |a XXI, 546 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs on statistics and applied probability |v 53 | |
| 650 | 4 | |a Assurance - Mathématiques | |
| 650 | 4 | |a Procesos estocásticos | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 4 | |a Riesgo (Seguros) | |
| 650 | 7 | |a Risicotheorie |2 gtt | |
| 650 | 4 | |a Risque (Assurance) | |
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 7 | |a Verzekeringswiskunde |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Insurance |x Mathematics | |
| 650 | 4 | |a Risk (Insurance) | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Risikotheorie |0 (DE-588)4135592-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Versicherungsmathematik |0 (DE-588)4063194-1 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006362417 | ||
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Datensatz im Suchindex
| _version_ | 1804123967155339264 |
|---|---|
| adam_text | Contents
Preface xi
Nomenclature xv
PART ONE FOUNDATIONS OF
PRACTICAL RISK THEORY
1 Some preliminary ideas 3
1.1 Cash flow and emerging costs 3
1.2 Accounting model 7
1.3 Some features of the classical theory 13
1.4 Notation and some concepts from probability
theory 18
2 The number of claims 30
2.1 Introduction 30
2.2 The Poisson distribution 31
2.3 Properties of Poisson variables 33
2.4 Mixed Poisson claim number variable 38
2.5 The Polya case: negative binomial distribution 48
2.6 Variation of risk propensity within the portfolio 51
3 The amount of claims 55
3.1 Compound aggregate claim amount model 55
3.2 Properties of compound distributions 58
3.3 The claim size distribution 69
3.4 Claims and reinsurance 100
4 Calculation of a compound claim d.f. F 119
4.1 Recursion formula for F 119
4.2 Approximate formulae for F 125
viii CONTENTS
5 Simulation 137
5.1 Introductory remarks 137
5.2 Random numbers 138
5.3 Simulation of claim numbers 141
5.4 Simulation of compound variables 143
5.5 Outlines for simulation of more complex
insurance processes 147
6 Applications involving short term claim fluctuation 155
6.1 Background to the short term fluctuation
problem 155
6.2 Evaluating the capital at risk 163
6.3 Rules for maximum retention 170
6.4 An application to rate making 178
6.5 Experience rating 179
6.6 Optimal risk sharing 189
PART TWO STOCHASTIC ANALYSIS OF
INSURANCE BUSINESS
7 Inflation 211
7.1 Introductory remarks 211
7.2 Inflation and insurance 214
7.3 Modelling inflation 218
8 Investment 226
8.1 Investment as part of the insurance business 226
8.2 Investment returns 230
8.3 Modelling investment prices and returns 239
8.4 The Wilkie model 242
8.5 Other model structures 250
8.6 Asset/liability considerations 263
9 Claims with an extended time horizon 277
9.1 Description of the problem 277
9.2 Claim number process 278
9.3 Claim amounts 282
9.4 Simulation of the claim process 285
9.5 The settlement of claims 289
9.6 Catastrophes 305
CONTENTS ix
10 Premiums 310
10.1 General framework 310
10.2 Theoretical background 311
10.3 Premiums in practice 316
11 Expenses, taxes and dividends 320
11.1 Expenses 320
11.2 Taxes 324
11.3 Dividends 325
12 The insurance process 327
12.1 Basic equation 327
12.2 Empirical observations 329
12.3 Business cycles, analysis of causes and
mechanisms 333
12.4 Simulation of the insurance process 343
13 Applications to long term processes 357
13.1 General features 357
13.2 Capital requirements of an insurance
company 363
13.3 Evaluation of an insurer s net retention limits 367
14 Managing uncertainty 369
14.1 Review of applications 369
14.2 Basic equations 371
14.3 The insurer and the market 373
14.4 Measuring and managing financial strength 382
14.5 Corporate planning 390
14.6 Public solvency control 397
15 Life insurance 408
15.1 Recapitulation of some basic formulae of life
insurance mathematics 408
15.2 Stochastic cohort approach 413
15.3 Analysis of the total business 426
16 Pension schemes 435
16.1 Pension structures and definitions 435
16.2 Pension formulae 436
x CONTENTS
16.3 Deterministic methods of pension funding 442
16.4 Stochastic methods for pensions 447
APPENDICES
A Derivation of the Poisson formula 452
A.I Individual and collective approaches 452
A.2 Derivation of the Poisson distribution law 454
B P6lya and Gamma distributions 459
C Asymptotic behaviour of the compound mixed
Poisson d.f. 462
D Numerical calculation of the normal d.f. 463
E Derivation of the recursion formula for F 465
F Simulation 468
F.I Uniformly distributed random numbers 468
F.2 Normally distributed random numbers 469
F.3 Graphical presentation of outcomes 469
F.4 Numerical outputs and their accuracy 470
F.5 Simulation of the insurance business 472
G Time series 476
G.I Basic concepts 476
G.2 Autoregressive process of first order 479
G.3 Autoregressive process of second order 481
G.4 Generalizations and variants 484
H Portfolio selection 488
I Solutions to exercises 492
Bibliography 514
Subject index 526
Author index 544
|
| any_adam_object | 1 |
| author | Daykin, Christopher D. Pentikäinen, Teivo 1917-2006 Pesonen, Martti |
| author_GND | (DE-588)170517632 (DE-588)170324826 |
| author_facet | Daykin, Christopher D. Pentikäinen, Teivo 1917-2006 Pesonen, Martti |
| author_role | aut aut aut |
| author_sort | Daykin, Christopher D. |
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| building | Verbundindex |
| bvnumber | BV009627147 |
| callnumber-first | H - Social Science |
| callnumber-label | HG8781 |
| callnumber-raw | HG8781 |
| callnumber-search | HG8781 |
| callnumber-sort | HG 48781 |
| callnumber-subject | HG - Finance |
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| classification_tum | MAT 902f |
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| dewey-full | 368/.01 |
| dewey-hundreds | 300 - Social sciences |
| 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 | 1. ed. |
| format | Book |
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| id | DE-604.BV009627147 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:11Z |
| institution | BVB |
| isbn | 0412428504 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006362417 |
| oclc_num | 28844823 |
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| physical | XXI, 546 S. graph. Darst. |
| publishDate | 1994 |
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| publisher | Chapman & Hall |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Daykin, Christopher D. Verfasser (DE-588)170517632 aut Practical risk theory for actuaries C. D. Daykin, T. Pentikäinen and M. Pesonen 1. ed. London [u.a.] Chapman & Hall 1994 XXI, 546 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 53 Assurance - Mathématiques Procesos estocásticos Processus stochastiques Riesgo (Seguros) Risicotheorie gtt Risque (Assurance) Stochastische processen gtt Verzekeringswiskunde gtt Mathematik Insurance Mathematics Risk (Insurance) Stochastic processes Risikotheorie (DE-588)4135592-1 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 s Risikotheorie (DE-588)4135592-1 s Stochastisches Modell (DE-588)4057633-4 s 1\p DE-604 Pentikäinen, Teivo 1917-2006 Verfasser (DE-588)170324826 aut Pesonen, Martti Verfasser aut Monographs on statistics and applied probability 53 (DE-604)BV002494005 53 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006362417&sequence=000002&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 | Daykin, Christopher D. Pentikäinen, Teivo 1917-2006 Pesonen, Martti Practical risk theory for actuaries Monographs on statistics and applied probability Assurance - Mathématiques Procesos estocásticos Processus stochastiques Riesgo (Seguros) Risicotheorie gtt Risque (Assurance) Stochastische processen gtt Verzekeringswiskunde gtt Mathematik Insurance Mathematics Risk (Insurance) Stochastic processes Risikotheorie (DE-588)4135592-1 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4135592-1 (DE-588)4063194-1 (DE-588)4057633-4 |
| title | Practical risk theory for actuaries |
| title_auth | Practical risk theory for actuaries |
| title_exact_search | Practical risk theory for actuaries |
| title_full | Practical risk theory for actuaries C. D. Daykin, T. Pentikäinen and M. Pesonen |
| title_fullStr | Practical risk theory for actuaries C. D. Daykin, T. Pentikäinen and M. Pesonen |
| title_full_unstemmed | Practical risk theory for actuaries C. D. Daykin, T. Pentikäinen and M. Pesonen |
| title_short | Practical risk theory for actuaries |
| title_sort | practical risk theory for actuaries |
| topic | Assurance - Mathématiques Procesos estocásticos Processus stochastiques Riesgo (Seguros) Risicotheorie gtt Risque (Assurance) Stochastische processen gtt Verzekeringswiskunde gtt Mathematik Insurance Mathematics Risk (Insurance) Stochastic processes Risikotheorie (DE-588)4135592-1 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Assurance - Mathématiques Procesos estocásticos Processus stochastiques Riesgo (Seguros) Risicotheorie Risque (Assurance) Stochastische processen Verzekeringswiskunde Mathematik Insurance Mathematics Risk (Insurance) Stochastic processes Risikotheorie Versicherungsmathematik Stochastisches Modell |
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