随机观测下两面跳的对偶风险模型

Dual Risk Model with Two-sided Jumps under Randomized Observation

主要研究随机观测下对偶风险模型的期望折现罚金函数.首先,利用过程的马尔可夫性得到了期望折现罚金函数所满足的积分微分方程.其次,当罚金函数取不同的值时,得到了破产时的Laplace变换、破产时赤字的期望折现函数以及破产概率所满足的积分微分方程.最后,给出了两面跳均服从指数分布情况下破产概率的显性表达式以及具体的数值例子.

This paper mainly studies the expected discounted penalty function of the dual risk model under randomized observation. Firstly, by using the Markov property of the process, the integral differential equation of the expected discounted penalty function is obtained. Then, the integral differential equations for the Laplace transform of the ruin time, the expected discounted function of the deficit at the ruin time and the ruin probability are derived when the penalty function takes different values. Finally, the closed-form expression and the specific numerical example of the ruin probability in the case of the exponential distribution are given.