带延迟索赔和随机收入的离散风险模型的Gerber-Shiu分析（英）

破产理论是保险数学中的重要问题，它可以为保险公司决策者提供一个非常有用的早期风险预警手段．本文研究了一个带潜在延迟索赔和随机保费收入的复合二项风险模型．利用矩母函数的技巧，得到了 Gerber-Shiu 期望折罚函数的递推公式．特别地，还得到了贴现因子为 1 的特殊情形下的 Gerber-Shiu 期望折罚函数的解析表达式．最后还得到了实际应用中的一些重要的破产特征量，包括破产概率，破产时赤字的密度函数，破产前盈余与破产时赤字的联合密度函数，以及导致破产的索赔密度函数等．

Gerber-Shiu Analysis for a Discrete Risk Model with Delayed Claims and Random Incomes

Ruin theory is the mainly contents of insurance mathematics,as it can supply a very useful early-warning measure for the risk of the insurance company.In this paper,we study a risk model with potentially delayed claims and random premium incomes within the framework of the compound binomial model.Using the technique of generating functions,we derive a recursive formula for the Gerber-Shiu expected discounted penalty function.Specifically,an explicit formula is obtained for the discount-free case.As applications,we derive some useful insurance quantities,including the ruin probability,the density of the deficit at ruin,the joint density of the surplus immediately before ruin and the deficit at ruin,and the density of the claim causing ruin.