中文摘要：

本文讨论由Markov环境过程驱动的风险过程,给出了期望贴现惩罚函数的Laplace变换的表达式,利用一般Lundberg基本方程,得到了期望贴现惩罚函数的简洁表达式,并推得了给定初始环境状态,初始资金为0时破产前瞬间盈余、破产赤字的贴现联合密度及其边缘密度。同时,本文也给出了破产时间、破产前瞬间盈余以及破产时赤字的矩的计算方法。

英文摘要：

In this paper,a risk model driven by Markovian environment process that affects both the claim sizes and rates is described.The expression of Laplace transform of the Gerber-Shiu function is obtained.By means of the general Lundberg fundamental equation,the explicit expressions for the Gerber-Shiu functions with zero initial capital,the given state of environment,the discounted joint density functions and the density marginal density of the surplus prior to and after ruin are derived,respectively.Meanwhile,the methods to compute the arbitrary moments of the time to ruin,surplus before ruin and the deficit at ruin are also given.