特殊索赔下离散时间延迟更新过程的期望贴现罚金函数

On the expected discounted penalty function in the discrete time delayed renewal process with special claims

离散时间更新风险过程下所获得的结果一般都具有递归的属性而易于程序化,因此不但具有独立的研究意义,还可以作为连续时间更新过程相关结果的近似和上下界估计.研究具有一般索赔间隔时间的离散时间延迟更新过程,在索赔额服从几何分布时,利用Lundberg基本方程的根及期望贴现罚金函数所满足的更新方程,获得了期望贴现罚金函数的显示表达.

Since formulas for discrete time models are of a recursive nature and readily programmable in practice, discrete time risk models are not only of independent interest but the results for them can also be used as approximations or bounds for the corresponding results in continuous time. In the present paper we investigate discrete time delayed renewal process with general inter-claim time. When the claim amounts follow geometrical distributions, by using the root of Lundberg equation and defective renewal equation satisfied by the discounted penalty function, we obtain some explicit