Insurance risk models
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Schaumburg, Ill.
Soc. of Actuaries
1992
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Panjer, Harry H. |d 1946- |e Verfasser |0 (DE-588)1044735732 |4 aut | |
| 245 | 1 | 0 | |a Insurance risk models |c Harry H. Panjer ; Gordon E. Willmot |
| 264 | 1 | |a Schaumburg, Ill. |b Soc. of Actuaries |c 1992 | |
| 300 | |a 442 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Assurance - Mathématiques - Modèles mathématiques | |
| 650 | 7 | |a Assurance - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Modellen |2 gtt | |
| 650 | 7 | |a Risicotheorie |2 gtt | |
| 650 | 4 | |a Risque (Assurance) - Modèles mathématiques | |
| 650 | 7 | |a Risque (assurance) - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Verzekeringswiskunde |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Insurance |x Mathematics |x Mathematical models | |
| 650 | 4 | |a Risk (Insurance) |x Mathematical models | |
| 650 | 0 | 7 | |a Versicherung |0 (DE-588)4063173-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Risiko |0 (DE-588)4050129-2 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-005469978 | |
Datensatz im Suchindex
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| DE-BY-UBR_call_number | 40/QQ 600 P193 |
| DE-BY-UBR_katkey | 2004601 |
| DE-BY-UBR_location | 40 |
| DE-BY-UBR_media_number | 069006148157 |
| _version_ | 1822659430925205504 |
| adam_text | TABLE OF CONTENTS
Preface ix
PART I: STATISTICAL PRELIMINARIES
1. Introduction and Mathematical Background 1
1.1 Introduction to the Book 1
1.2 Ordinary Generating Functions 3
1.3 Laplace Transforms 9
1.4 Bibliographic Notes 16
Exercises 16
2. Probability and Random Variables 23
2.1 Introduction 23
2.2 Random Variables 23
2.3 Expected Values of Random Variables 27
2.4 Generating Functions and Transforms 32
2.5 Conditional Distributions 37
2.6 Sums of Random Variables 39
2.7 Infinite Divisibility 41
2.8 Mixtures of Distributions 47
2.9 Distribution of Random Sums 50
2.10 Order Statistics 55
2.11 Central Limit Theorem 58
2.12 Bibliographic Notes 59
3. Stochastic Processes 61
3.1 Introduction 61
3.2 Stochastic Processes 61
3.3 The Poisson Process 63
3.4 The Nonhomogeneous Poisson Process 69
3.5 The Mixed Poisson Process 72
3.6 Birth Processes 73
3.7 Compound Stochastic Processes 82
3.8 Bibliographic Notes 83
4. Probability Distributions 85
4.1 Introduction 85
4.2 The Poisson Distribution 85
4.3 The Binomial Distribution 87
4.4 The Geometric Distribution 89
4.5 The Negative Binomial Distribution 90
4.6 The Logarithmic Distribution 92
4.7 Mixed and Compound Discrete Distributions 95
4.8 Other Discrete Distributions 98
4.9 The Exponential Distribution 100
4.10 The Pareto Distribution 104
4.11 The Lognormal Distribution 109
4.12 The Gamma Distribution 111
4.13 The Inverse Gaussian Distribution 114
4.14 Other Continuous Distributions 117
4.15 Bibliographic Notes 125
PART II: BASIC RISK MODELS
5. Individual Risk Models 127
5.1 Introduction 127
5.2 The Model 127
5.3 Evaluation of the Distribution of Total Claims 137
5.4 Life Insurance 139
5.5 Approximations to the Distribution of Total Claims 148
5.6 Reinsurance 151
5.7 Bibliographic Notes 158
Exercises 159
6. Basic Compound Risk Models 165
6.1 Introduction 165
6.2 The Compound Poisson Distribution 169
6.3 Combining Compound Poisson Risks 175
6.4 Decomposing Compound Poisson Risks 179
6.5 Approximating the Individual Risk Model by the
Compound Poisson Model 188
6.6 Computation for Arithmetic Severities 193
6.7 Compound Negative Binomial as a Mixture 201
6.8 Compound Negative Binomial as a Compound
Poisson with Multiple Claims 209
6.9 Compound Negative Binomial as a Contagion Model 212
6.10 Compound Binomial as a Closed Group Model 213
6.11 Compound Binomial as a Contagion Model 213
6.12 Analytic Results for Certain Claim Size Distributions 214
6.13 Removal of Zero Claims 218
6.14 Computation for Continuous Severities 221
6.15 Computational Techniques for Non Arithmetic Severities 223
6.16 Modification of the Claim Number Distribution 230
6.17 Reinsurance 234
6.18 Bibliographic Notes 236
Exercises 237
PART III: ADVANCED RISK MODELS
7. Compound Claim Frequency Models 243
7.1 Introduction 243
7.2 The (a,b) Class of Distributions 247
7.3 Compound Poisson Claim Frequency Models 255
7.4 Neyman Type A Distribution 257
7.5 Generalized Poisson Pascal Distribution 259
7.6 One Parameter Primary and Modified Distributions 262
7.7 Other Compound Distributions 266
7.8 Removal of Zero Claims 267
7.9 Bibliographic Notes 268
Exercises 269
8. Mixed Claim Frequency Models 271
8.1 Introduction 271
8.2 Mixed Poisson Distributions 273
8.3 The Poisson Inverse Gaussian Distribution 279
8.4 Other Mixed Models 285
8.5 Other Frequency Models 287
8.6 Bibliographic Notes 287
Exercises 288
PART IV: FITTING, ESTIMATING AND APPROXIMATING
9. Fitting Risk Models 291
9.1 Introduction 291
9.2 Model Selection 292
9.3 Methods of Estimation 295
9.4 Testing the Fit of the Model 298
9.5 Sample Data Sets 300
9.6 Moment Estimation 301
9.7 Ad Hoc Estimation 303
9.8 Maximum Likelihood Estimation 305
9.9 MLE for Power Series Distributions 314
9.10 MLE for Some Other Frequency Models 317
9.11 Estimation for the Generalized Poisson Pascal 324
9.12 Other Fitting Problems 332
9.13 Bibliographic Notes 332
Exercises 333
10. Tail Behaviour of the Aggregate Claims Distribution 339
10.1 Introduction 339
10.2 Tail Behaviour for Certain Claim Number Models 339
10.3 Tail Behaviour for Certain Severity Models 345
10.4 Bibliographic Notes 351
Exercises 352
PARTV: RUIN THEORY
11. Ruin Probability Calculations 357
11.1 Introduction 357
11.2 Quantities of Interest 358
11.3 The Adjustment Coefficient 359
11.4 An Explicit Formula 365
11.5 Special Claim Amount Distributions 373
11.6 Asymptotic Results 384
11.7 Ruin over a Finite Interval 388
11.8 Bibliographic and Other Notes 399
Exercises 400
Appendix A The Gamma and Incomplete Gamma Functions 407
Appendix B The Incomplete Beta Function 411
Appendix C The Modified Bessel Function of the Third Kind 413
Appendix D Numerical Solutions of Integral Equations 415
References 425
Index 439
|
| any_adam_object | 1 |
| author | Panjer, Harry H. 1946- Willmot, Gordon E. 1957- |
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| dewey-ones | 368 - Insurance |
| dewey-raw | 368/.01 |
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| dewey-tens | 360 - Social problems and services; associations |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV008278772 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T12:43:34Z |
| institution | BVB |
| isbn | 0938959255 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005469978 |
| oclc_num | 25873232 |
| open_access_boolean | |
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| owner_facet | DE-384 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-824 DE-91G DE-BY-TUM DE-11 |
| physical | 442 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Soc. of Actuaries |
| record_format | marc |
| spellingShingle | Panjer, Harry H. 1946- Willmot, Gordon E. 1957- Insurance risk models Assurance - Mathématiques - Modèles mathématiques Assurance - Modèles mathématiques ram Modellen gtt Risicotheorie gtt Risque (Assurance) - Modèles mathématiques Risque (assurance) - Modèles mathématiques ram Verzekeringswiskunde gtt Mathematik Mathematisches Modell Insurance Mathematics Mathematical models Risk (Insurance) Mathematical models Versicherung (DE-588)4063173-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Risiko (DE-588)4050129-2 gnd |
| subject_GND | (DE-588)4063173-4 (DE-588)4114528-8 (DE-588)4050129-2 |
| title | Insurance risk models |
| title_auth | Insurance risk models |
| title_exact_search | Insurance risk models |
| title_full | Insurance risk models Harry H. Panjer ; Gordon E. Willmot |
| title_fullStr | Insurance risk models Harry H. Panjer ; Gordon E. Willmot |
| title_full_unstemmed | Insurance risk models Harry H. Panjer ; Gordon E. Willmot |
| title_short | Insurance risk models |
| title_sort | insurance risk models |
| topic | Assurance - Mathématiques - Modèles mathématiques Assurance - Modèles mathématiques ram Modellen gtt Risicotheorie gtt Risque (Assurance) - Modèles mathématiques Risque (assurance) - Modèles mathématiques ram Verzekeringswiskunde gtt Mathematik Mathematisches Modell Insurance Mathematics Mathematical models Risk (Insurance) Mathematical models Versicherung (DE-588)4063173-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Risiko (DE-588)4050129-2 gnd |
| topic_facet | Assurance - Mathématiques - Modèles mathématiques Assurance - Modèles mathématiques Modellen Risicotheorie Risque (Assurance) - Modèles mathématiques Risque (assurance) - Modèles mathématiques Verzekeringswiskunde Mathematik Mathematisches Modell Insurance Mathematics Mathematical models Risk (Insurance) Mathematical models Versicherung Risiko |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005469978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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