## Non-Life Insurance MathematicsThe book gives a comprehensive overview of modern non-life actuarial science. It starts with a verbal description (i.e. without using mathematical formulae) of the main actuarial problems to be solved in non-life practice. Then in an extensive second chapter all the mathematical tools needed to solve these problems are dealt with - now in mathematical notation. The rest of the book is devoted to the exact formulation of various problems and their possible solutions. Being a good mixture of practical problems and their actuarial solutions, the book addresses above all two types of readers: firstly students (of mathematics, probability and statistics, informatics, economics) having some mathematical knowledge, and secondly insurance practitioners who remember mathematics only from some distance. Prerequisites are basic calculus and probability theory. |

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### Contents

Problems | 1 |

Tools | 7 |

22 Distributions for K and X | 16 |

23 Moments | 21 |

24 The Total Claims Cost Z | 29 |

25 Cramers Inequality | 36 |

26 Dependent Variables | 42 |

Premiums | 52 |

Reinsurance | 68 |

Retentions | 76 |

Statistics | 89 |

Reserves | 102 |

Solutions | 116 |

82 Exact Credibility | 119 |

83 Closing the Circle | 126 |

131 | |

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### Common terms and phrases

accident assumed average ball basic called catastrophe ceding company central moments Chain Ladder method Chapter coefficients Cramer's inequality degenerated distribution denote density estimator exact pure risk example excess of loss expected value experience rating exponential utility exponentially distributed final loss fluctuations formula function Gamma distribution gross claim IBNR reserves independent individual claims amount initial reserves iteration iteration iteration lag factors linear London Chain loss ratio loss reinsurance loss treaties means million moment generating function Motor Liability negative binomial distribution Non-Life actuarial non-proportional number of claims overall parameter Pareto distributions Poisson distribution portfolio posterior practice premium calculation principle Prob Prob[K problem profit margin pure risk premium quota share random variable reinsurer pays risk aversion risk class risk willingness ruin probability rule so-called solution statistics stochastic stop loss sum insured surplus tariff theory total claims cost total of claims trapezoid with exact unbalancedness Var[Z variance yields

### Popular passages

Page 131 - Barlow R., Proschan F., Statistical Theory of Reliability and Life Testing, Holt, Rinehart and Winston, New York, 1975 [2] Comtet L., Advanced Combinatorics, D.