Risk Theory

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Springer, Apr 4, 2018 - Business & Economics - 242 pages

This book provides an overview of classical actuarial techniques, including material that is not readily accessible elsewhere such as the Ammeter risk model and the Markov-modulated risk model. Other topics covered include utility theory, credibility theory, claims reserving and ruin theory. The author treats both theoretical and practical aspects and also discusses links to Solvency II.

Written by one of the leading experts in the field, these lecture notes serve as a valuable introduction to some of the most frequently used methods in non-life insurance. They will be of particular interest to graduate students, researchers and practitioners in insurance, finance and risk management.

 

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Contents

1 Risk Models
1
2 Utility Theory
35
3 Credibility Theory
47
4 Claims Reserving
71
5 The CramérLundberg Model
83
6 The Renewal Risk Model
131
7 The Ammeter Risk Model
149
8 Change of Measure Techniques
169
Appendix B Martingales
199
Appendix C Renewal Processes
201
Appendix D Brownian Motion
211
Appendix E Random Walks and the WienerHopf Factorisation
213
Appendix F Subexponential Distributions
217
Appendix G Concave and Convex Functions
225
Appendix Table of Distribution Functions
229
Appendix References
233

9 The Markov Modulated Risk Model
183
A Stochastic Processes
197

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About the author (2018)

Hanspeter Schmidli is Professor of Stochastics and Actuarial Mathematics at the University of Cologne, Germany. He is one of the leading experts in the areas of optimization in insurance and ruin theory. He has published intensively in risk theory and related fields, having (co-)authored Stochastic Control in Insurance (Springer, 2008) and Stochastic Processes for Insurance and Finance (Wiley, 1999), which continue to be widely used resources.

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