Insurance risk and ruin:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2005
|
| Edition: | 1. publ. |
| Series: | International series on actuarial science
|
| Subjects: | |
| Online Access: | Table of contents Publisher description Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 229 S. graph. Darst. |
| ISBN: | 0521846404 9780521846400 9780521176750 |
Staff View
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| 100 | 1 | |a Dickson, David C. M. |e Verfasser |4 aut | |
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Record in the Search Index
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| adam_text | Contents
Preface page xi
1 Probability distributions and insurance applications 1
1.1 Introduction 1
1.2 Important discrete distributions 2
1.3 Important continuous distributions 5
1.4 Mixed distributions 9
1.5 Insurance applications 11
1.6 Sums of random variables 18
1.7 Notes and references 23
1.8 Exercises 24
2 Utility theory 27
2.1 Introduction 27
2.2 Utility functions 27
2.3 The expected utility criterion 28
2.4 Jensen s inequality 29
2.5 Types of utility function 31
2.6 Notes and references 36
2.7 Exercises 36
3 Principles of premium calculation 38
3.1 Introduction 38
3.2 Properties of premium principles 38
3.3 Examples of premium principles 39
3.4 Notes and references 50
3.5 Exercises 50
4 The collective risk model 52
4.1 Introduction 52
vii
4.2 The model 53
4.3 The compound Poisson distribution 56
4.4 The effect of reinsurance 59
4.5 Recursive calculation of aggregate claims distributions 64
4.6 Extensions of the Panjer recursion formula 72
4.7 The application of recursion formulae 79
4.8 Approximate calculation of aggregate claims distributions 83
4.9 Notes and references 89
4.10 Exercises 89
5 The individual risk model 93
5.1 Introduction 93
5.2 The model 93
5.3 De Pril s recursion formula 94
5.4 Kornya s method 97
5.5 Compound Poisson approximation 101
5.6 Numerical illustration 105
5.7 Notes and references 108
5.8 Exercises 108
6 Introduction to ruin theory 112
6.1 Introduction 112
6.2 A discrete time risk model 113
6.3 The probability of ultimate ruin 114
6.4 The probability of ruin in finite time 118
6.5 Lundberg s inequality 120
6.6 Notes and references 123
6.7 Exercises 123
7 Classical ruin theory 125
7.1 Introduction 125
7.2 The classical risk process 125
7.3 Poisson and compound Poisson processes 127
7.4 Definitions of ruin probability 129
7.5 The adjustment coefficient 130
7.6 Lundberg s inequality 133
7.7 Survival probability 135
7.8 The Laplace transform of j 138
7.9 Recursive calculation 142
7.10 Approximate calculation of ruin probabilities 151
7.11 Notes and references 153
7.12 Exercises 154
8 Advanced ruin theory 157
8.1 Introduction 157
8.2 A barrier problem 157
8.3 The severity of ruin 158
8.4 The maximum severity of ruin 163
8.5 The surplus prior to ruin 165
8.6 The time of ruin 172
8.7 Dividends 180
8.8 Notes and references 186
8.9 Exercises 187
9 Reinsurance 190
9.1 Introduction 190
9.2 Application of utility theory 190
9.3 Reinsurance and ruin 194
9.4 Notes and references 205
9.5 Exercises 206
References 208
Solution to exercises 211
Index 227
|
| adam_txt |
Contents
Preface page xi
1 Probability distributions and insurance applications 1
1.1 Introduction 1
1.2 Important discrete distributions 2
1.3 Important continuous distributions 5
1.4 Mixed distributions 9
1.5 Insurance applications 11
1.6 Sums of random variables 18
1.7 Notes and references 23
1.8 Exercises 24
2 Utility theory 27
2.1 Introduction 27
2.2 Utility functions 27
2.3 The expected utility criterion 28
2.4 Jensen's inequality 29
2.5 Types of utility function 31
2.6 Notes and references 36
2.7 Exercises 36
3 Principles of premium calculation 38
3.1 Introduction 38
3.2 Properties of premium principles 38
3.3 Examples of premium principles 39
3.4 Notes and references 50
3.5 Exercises 50
4 The collective risk model 52
4.1 Introduction 52
vii
4.2 The model 53
4.3 The compound Poisson distribution 56
4.4 The effect of reinsurance 59
4.5 Recursive calculation of aggregate claims distributions 64
4.6 Extensions of the Panjer recursion formula 72
4.7 The application of recursion formulae 79
4.8 Approximate calculation of aggregate claims distributions 83
4.9 Notes and references 89
4.10 Exercises 89
5 The individual risk model 93
5.1 Introduction 93
5.2 The model 93
5.3 De Pril's recursion formula 94
5.4 Kornya's method 97
5.5 Compound Poisson approximation 101
5.6 Numerical illustration 105
5.7 Notes and references 108
5.8 Exercises 108
6 Introduction to ruin theory 112
6.1 Introduction 112
6.2 A discrete time risk model 113
6.3 The probability of ultimate ruin 114
6.4 The probability of ruin in finite time 118
6.5 Lundberg's inequality 120
6.6 Notes and references 123
6.7 Exercises 123
7 Classical ruin theory 125
7.1 Introduction 125
7.2 The classical risk process 125
7.3 Poisson and compound Poisson processes 127
7.4 Definitions of ruin probability 129
7.5 The adjustment coefficient 130
7.6 Lundberg's inequality 133
7.7 Survival probability 135
7.8 The Laplace transform of j 138
7.9 Recursive calculation 142
7.10 Approximate calculation of ruin probabilities 151
7.11 Notes and references 153
7.12 Exercises 154
8 Advanced ruin theory 157
8.1 Introduction 157
8.2 A barrier problem 157
8.3 The severity of ruin 158
8.4 The maximum severity of ruin 163
8.5 The surplus prior to ruin 165
8.6 The time of ruin 172
8.7 Dividends 180
8.8 Notes and references 186
8.9 Exercises 187
9 Reinsurance 190
9.1 Introduction 190
9.2 Application of utility theory 190
9.3 Reinsurance and ruin 194
9.4 Notes and references 205
9.5 Exercises 206
References 208
Solution to exercises 211
Index 227 |
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| isbn | 0521846404 9780521846400 9780521176750 |
| language | English |
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| spelling | Dickson, David C. M. Verfasser aut Insurance risk and ruin David C. M. Dickson 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2005 XII, 229 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series on actuarial science Hier auch später erschienene, unveränderte Nachdrucke Assurance - Mathématiques Risk management gtt Risque (Assurance) - Modèles mathématiques Speltheorie gtt Stochastische processen gtt Atuária larpcal Risco larpcal Seguro (modelos matemáticos) larpcal Mathematik Mathematisches Modell Insurance Mathematics Risk (Insurance) Mathematical models Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 s DE-604 http://www.loc.gov/catdir/toc/cam051/2004054520.html Table of contents http://www.loc.gov/catdir/description/cam051/2004054520.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014278898&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dickson, David C. M. Insurance risk and ruin Assurance - Mathématiques Risk management gtt Risque (Assurance) - Modèles mathématiques Speltheorie gtt Stochastische processen gtt Atuária larpcal Risco larpcal Seguro (modelos matemáticos) larpcal Mathematik Mathematisches Modell Insurance Mathematics Risk (Insurance) Mathematical models Versicherungsmathematik (DE-588)4063194-1 gnd |
| subject_GND | (DE-588)4063194-1 |
| title | Insurance risk and ruin |
| title_auth | Insurance risk and ruin |
| title_exact_search | Insurance risk and ruin |
| title_exact_search_txtP | Insurance risk and ruin |
| title_full | Insurance risk and ruin David C. M. Dickson |
| title_fullStr | Insurance risk and ruin David C. M. Dickson |
| title_full_unstemmed | Insurance risk and ruin David C. M. Dickson |
| title_short | Insurance risk and ruin |
| title_sort | insurance risk and ruin |
| topic | Assurance - Mathématiques Risk management gtt Risque (Assurance) - Modèles mathématiques Speltheorie gtt Stochastische processen gtt Atuária larpcal Risco larpcal Seguro (modelos matemáticos) larpcal Mathematik Mathematisches Modell Insurance Mathematics Risk (Insurance) Mathematical models Versicherungsmathematik (DE-588)4063194-1 gnd |
| topic_facet | Assurance - Mathématiques Risk management Risque (Assurance) - Modèles mathématiques Speltheorie Stochastische processen Atuária Risco Seguro (modelos matemáticos) Mathematik Mathematisches Modell Insurance Mathematics Risk (Insurance) Mathematical models Versicherungsmathematik |
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