支付红利的双险种复合二项风险模型的Gerber-Shiu折现罚金函数

摘要

In this paper,we study the double type-insurance compound binomial risk model. The insurer pays dividends to shareholders with a probability when the surplus is greater than or e-qual to a non-negative dividend-line. We derive the defective renewal equation and the asymptotic expressions for the Gerber-Shiu discounted penalty function by using the renewal theory. The recursion formulas and asymptotic expressions for the ruin probability, the probability function of the severity of ruin,and the surplus prior to the ruin time are obtained.%对支付红利的双险种复合二项模型,考虑当盈余大于或等于一个给定的非负红利界时保险公司以一定概率给股东分红的情形,利用更新理论,得到该模型的Gerber-Shiu折现罚金函数满足的瑕疵更新方程及其渐近表达式,并给出破产概率、破产时破产赤字分布和破产前瞬时盈余的概率函数的递推公式及其渐近表达式.