The maximum surplus distribution before ruin in an Erlang(n) risk process perturbed by diffusion

被引：0

作者：

Zhen Zhong Zhang

Jie Zhong Zou

Yuan Yuan Liu

机构：

[1] Donghua University,College of Science

[2] Central South University,School of Mathematics

来源：

Acta Mathematica Sinica, English Series | 2011年 / 27卷

关键词：

Sparre Anderson risk model; generalized Erlang(; ) inter-claim times; integro-differential equation; diffusion process; maximum surplus distribution; 91B30; 91B60;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang(n) risk process (i.e., convolution of n exponential distributions with possibly different parameters) perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented.

引用

页码：1869 / 1880

页数：11

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