RISK THEORY FOR THE COMPOUND POISSON-PROCESS THAT IS PERTURBED BY DIFFUSION

被引：209

作者：

DUFRESNE, F ^{[1
]}

GERBER, HU ^{[1
]}

机构：

[1] UNIV LAUSANNE,CH-1015 LAUSANNE,SWITZERLAND

来源：

INSURANCE MATHEMATICS & ECONOMICS | 1991年 / 10卷 / 01期

关键词：

RUIN THEORY; RISK THEORY; RENEWAL EQUATION; CONVOLUTION FORMULA; DIFFUSION; COMBINATIONS OF EXPONENTIAL CLAIM AMOUNTS;

D O I：

10.1016/0167-6687(91)90023-Q

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

The classical model of collective risk theory is extended in that a diffusion process is added to the compound Poisson process. It is shown that the probabilities of ruin (by oscillation or by a claim) satisfy certain defective renewal equations. The convolution formula for the probability of ruin is derived and interpreted in terms of the record highs of the aggregate loss process. If the distribution of the individual claim amounts are combinations of exponentials, the probabilities of ruin can be calculated in a transparent fashion. Finally, the role of the adjustment coefficient (for example, for the asymptotic formulas) is explained.

引用

页码：51 / 59

页数：9