## Premium Calculation in InsuranceF. Etienne De Vylder, Marc Goovaerts, J. Haezendonck I am pleased to participate in this Summer School and look forward to sharing some ideas with you over the next few days. At the outset I would like to describe the approach I will take in 1 presenting the material. I aim to present the material in a non rigorous way and hopefully in an intuitive manner. At the same time I will draw attention to some of the major technical problems. It is pitched at someone who is unfamiliar with the area. The results presented here are unfamiliar to actuaries and insurance mathematicians although they are well known in some other fields. During the next few minutes I will make some preliminary comments. The purpose of these comments is to place the lectures in perspective and motivate the upcoming material. After this I will outline briefly the topics to be covered during the rest of this lecture and in the lectures that will follow. One of the central themes of these lectures is RISK-SHARING. Risk-sharing is a common response to uncertainty. Such uncertainty can arise from natural phenomena or social causes. One particular form of risk-sharing is the insurance mechanism. I will be dealing with models which have a natural application in the insurance area but they have been applied in other areas as well. In fact some of the paradigms to be discussed have the capacity to provide a unified treatment of problems in diverse fields. |

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### Contents

19 | |

Statedependent utility the demand for insurance | 76 |

Separation of risk parameters | 109 |

Practical models in credibility theory including | 133 |

Rate making and the societys sense of fairness | 151 |

The impact of reinsurance on the insurers risk | 170 |

Net stop10ss ordering and related orderings | 194 |

Limit theorems for risk processes | 235 |

estimation of structural parameters | 347 |

Population and social security projections for Bangladesh | 363 |

Stability of premium principles under maximum entropy | 381 |

Motor premium rating | 398 |

The mean square error of a randomly discounted sequence | 449 |

Simulation in actuaria1 work Some computational | 466 |

The actuary in practice | 489 |

Some BerryEsseen theorems for risk processes | 505 |

estimation large sample theory | 262 |

Rating of non proportional reinsurance treaties based | 285 |

Resistant line fitting in actuarial science | 315 |

Quantitative models of pension costs | 333 |

### Other editions - View all

Premium Calculation in Insurance F. Etienne De Vylder,Marc Goovaerts,J. Haezendonck No preview available - 1984 |

Premium Calculation in Insurance F. Etienne De Vylder,Marc Goovaerts,J. Haezendonck No preview available - 2014 |

Premium Calculation in Insurance F. Etienne De Vylder,Marc Goovaerts,J. Haezendonck No preview available - 2011 |

### Common terms and phrases

agent's analysis annuity application assume assumptions average Bangladesh Bayes benefits Black–Scholes Calculation in Insurance claim frequency claim number claims cost compound Poisson distribution computed condition consider contract covariance matrix credibility defined denote economic equation error estimation example excess of loss expected utility expenses formula gamma distribution given Group Hence increase inflation insured wage largest claims liability linear Markov mathematical matrix mean method moral hazard normal distribution observable obtain optimal option parameter Pareto optimal payments pension funds Poisson portfolio Premium Calculation premium rates probability problem Proof random variables regression Reidel Publishing Company reinsurance reinsurance treaties risk aversion safety semi-Markov semi-Markov process sharing rule simulation solution statistical stochastic stochastic dominance stop-loss Table Theorem tion treaty utility function variance vector weighted Wylder