【作者】 张伟；

【导师】 赵明清；

【作者基本信息】 山东科技大学 ， 概率论与数理统计， 2010， 硕士

【摘要】 在风险相依的条件下,对于破产概率问题的研究目前已经成为风险理论的一个重要研究方向.本文对以下两类相依风险的破产问题进行了研究：第一,考虑了一类离散相依的风险模型,该模型假设主索赔以一定的概率引起两种副索赔,而第一种副索赔有可能延迟发生.通过引入一个辅助模型,对破产前盈余和破产时赤字进行分析得到了其联合分布递推公式、初始盈余为0时的最终破产概率表达式,并结合保险实例进行了数值模拟.第二,考虑了一类索赔额相依的风险模型,该模型假设主索赔达到一定的额度会产生一副索赔,而每次副索赔有可能延迟发生.通过引入辅助模型,得到了破产前盈余和破产时赤字的联合分布的递推公式、初始盈余为0时最终破产概率的表达式,并结合保险实例进行了数值模拟.更多还原

【Abstract】 At present, the study of ruin probability under correlated risk is becoming more and more important in risk areas.This thesis is devoted to the study of two kinds of correlated discrete risk model, it contains:Firstly, the discrete risk model with correlated claims is considered.Every mainclaim may produce two kinds of deputy claim and the occurrence of the first kind of deputy claim may be delayed.By means of auxiliary model,we obain the recursive formula of the joint distribution of the surplus immediately before ruin and deficit at ruin.Furthermore,the explicit expression for the probability is given when the initial surplus is zero.Finally,we show some numerical results according to the insurance case.Secondly,the model with correlated claims in which every claim can produce a deputy claim according to the amout of it is considered,the deputy claim may be delayed.By means of auxiliary model, we obain the recursive formula of the joint distribution of the surplus immediately before ruin and deficit at ruin.Furthermore,the explicit expression for the probability is given when the initial surplus is zero.Finally,we show some numerical results according to the insurance case.更多还原