离散索赔额的更新风险模型

贴现惩罚函数是保险公司破产前瞬间盈余和破产时赤字的函数,本文考虑了贴现惩罚函数在离散个体索赔额的复合Poisson更新风险模型中的应用.以鞅方法为基础,主要推导了贴现惩罚函数的具体更新方程表达式,以及渐进结果;而且还推导了破产前瞬间盈余和破产时赤字联合密度函数、破产时刻的条件期望和破产概率.最后得到了本文结果与经典风险模型的形式一致.

Renewal risk model of discrete claim amount

The discounted penalty function is the function of surplus immediately prior to ruin and deficit at ruin in an insurance company.This paper studies the application of the discounted penalty function in the Poisson renewal risk model,where the individual claim amount distribution is discrete.On the basis of martingale method,we show the explicit renewal function and its approximation.Explicit answers are obtained for the joint probability density function,the conditional expected time to ruin and the ruin probability.Moreover,it is concluded that the expression of functions in the compound Poisson renewal risk model inhere the invariable forms.