Buch, Englisch, 368 Seiten, Format (B × H): 177 mm x 252 mm, Gewicht: 700 g
Actuarial and Statistical Aspects
Buch, Englisch, 368 Seiten, Format (B × H): 177 mm x 252 mm, Gewicht: 700 g
Reihe: Wiley Series in Probability and Statistics
ISBN: 978-0-470-77268-3
Verlag: John Wiley & Sons Inc
Reinsurance: Actuarial and Statistical Aspects provides a survey of both the academic literature in the field as well as challenges appearing in reinsurance practice and puts the two in perspective. The book is written for researchers with an interest in reinsurance problems, for graduate students with a basic knowledge of probability and statistics as well as for reinsurance practitioners. The focus of the book is on modelling together with the statistical challenges that go along with it. The discussed statistical approaches are illustrated alongside six case studies of insurance loss data sets, ranging from MTPL over fire to storm and flood loss data. Some of the presented material also contains new results that have not yet been published in the research literature. An extensive bibliography provides readers with links for further study.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preface ix
1 Introduction 1
1.1 What is Reinsurance? 1
1.2 Why Reinsurance? 2
1.3 Reinsurance Data 4
1.3.1 Case Study I: Motor Liability Data 5
1.3.2 Case Study II: Dutch Fire Insurance Data 10
1.3.3 Case Study III: Austrian Storm Claim Data 10
1.3.4 Case Study IV: European Flood Risk Data 11
1.3.5 Case Study V: Groningen Earthquakes 12
1.3.6 Case Study VI: Danish Fire Insurance Data 12
1.4 Notes and Bibliography 16
2 Reinsurance Forms and their Properties 19
2.1 Quota-share Reinsurance 19
2.1.1 Some Practical Considerations 20
2.2 Surplus Reinsurance 21
2.3 Excess-of-loss Reinsurance 24
2.3.1 Moment Calculations 25
2.3.2 Reinstatements 27
2.3.3 Further Practical Considerations 29
2.4 Stop-loss Reinsurance 30
2.5 Large Claim Reinsurance 31
2.6 Combinations of Reinsurance Forms and Global Protections 32
2.7 Facultative Contracts 33
2.8 Notes and Bibliography 33
3 Models for Claim Sizes 35
3.1 Tails of Distributions 35
3.2 Large Claims 36
3.3 Common Claim Size Distributions 40
3.3.1 Light-tailed Models 41
3.3.2 Heavy-tailed Models 44
3.4 Mean Excess Analysis 49
3.5 Full Models: Splicing 50
3.6 Multivariate Modelling of Large Claims 52
4 Statistics for Claim Sizes 59
4.1 Heavy or Light Tails: QQ- and Derivative Plots 60
4.2 Large Claims Modelling through Extreme Value Analysis
EVA for Pareto-type Tails 63
4.2.1 EVA for Pareto-type Tails 63
4.2.2 General Tail Modelling using EVA 82
4.2.3 EVA under Upper-truncation 91
4.3 Global Fits: Splicing, Upper-truncation and Interval Censoring 97
4.3.1 Tail-mixed Erlang Splicing 97
4.3.2 Tail-mixed Erlang Splicing under Censoring and Upper-truncation 99
4.4 Incorporating Covariate Information 114
4.4.1 Pareto-type Modelling 114
