投资收益总额为poisson过程的风险模型

通过讨论投资收益总额为复合poisson过程的风险模型,得到了其Gerber-Shiu折现罚金函数满足的积分-微分方程,并且在索赔额和收益额的分布为指数分布的情况下得到了Gerber-Shiu折现罚金函数及其相关精算量满足的微分方程。

The Ruin Probability of Aggregate Returns on Investments with a Poisson Process

Through the discussion of the model which the aggregate investments is a compound poisson process,the integral differential equation of the Gerber-Shiu discounted penalty function is derived。 Furtrhermore,the differential equation of the Gerber-Shiu discounted penalty function and the related actuarial randoms are also obtained under the distributions of the claim and the returns of investment are exponential distributions。