Poisson过程及其稀疏过程在保险公司破产问题中的应用

Ruin Problem for The Poisson Processes and p—Thinning Processes

研究一类风险过程 ,其中保单的到达过程是一个强度为λ的Poisson过程 ,索赔的出现过程是保单到达过程的p———稀疏过程。对此风险过程给出了破产概率的Lundberg不等式以及Lundberg指数 。

In this paper, we consider a risk processes that can be used to describe a class of life or nor-life risk models, where the arrival of term policies follows a Poisson processes and the arrival of the claims follows a p—thinning Processes. We obtain the Lundberg inequality for the ruin probability. We will compare the size of the Lundberg exponents for different kinds of risk model. We also consider the numerical illustration for the impact of the parameters on the ruin probability.