指数索赔下带有分红和随机保费相依模型的破产概率

Ruin Probability of Dependent Risk Model with Stochastic Premiums and Threshold Divided under Exponential Claims

摘要: 本文研究了具有随机保费和阈值分红的风险模型，其中保费收入为复合泊松过程，而索赔额和索赔间隔时间具有特殊的相依结构。利用平稳独立增量性质，得到了破产概率和破产前期望贴现红利的积分方程。此外，当随机保费和索赔额均服从指数分布时，可以得到破产概率特征方程以及破产前期望贴现红利特征方程的根。

Abstract: The paper considers a risk model with stochastic premiums and threshold dividends, where premium income is a compound composite Poisson process and a specific dependent structure are assumed between claim sizes and inter-claim times. By utilizing the stationary and independent increment property, we derive the integral equation for ruin probability and the expected discounted dividend payments until ruin. In addition, when stochastic premium and claim amount are exponentially distributed, we can derive roots of the characteristic equation of ruin probability and the expected discounted dividend payments until ruin respectively.