## Risk TheoryThis 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

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 |

### Other editions - View all

### Common terms and phrases

adjustment coefficient Ammeter Ammeter risk model Assume Bibliographical Remarks claim size distribution coherent risk measure compound Poisson compound Poisson distribution concave function consider converges convex Cramér–Lundberg approximation credibility denote density differentiable directly Riemann integrable distributed claim distribution function Eoſe equation estimator Example exists expected value exponentially distributed IE[S independent initial capital intensity interval IPIT ladder height Lemma loss Lundberg exponent Lundberg’s inequality Markov martingale measure Q moment generating function negative binomial distribution Note number of claims obtain parameter Poisson process premium profit condition Proof Let random variable reinsurance renewal risk model Riemann integrable risk exchange risk measure Risk Theory risk volume ruin probability Schmidli ſº solution Springer Actuarial Springer International Publishing Springer Nature 2017 stochastic process strictly positive subexponential u-Hct utility function Var(X variance yields