基于鞅方法的连续时间复合二项风险模型破产问题分析

Analysis of problem of a ruin on continuous-time compound binomial model based on approach of martingal

作为离散时间复合二项模型的连续化版本,连续时间复合二项模型的极限形式即为经典风险模型.先将风险模型纳入PDMP框架,借助广义生成算子理论,推导出模型期望折扣罚函数满足的(脉冲)积分微分方程,并对初始准备金为整数的情形给出其满足的迭代公式,最后得到模型破产概率满足的表达式.

The continuous-time compound binomial model is the continuous-time version of the compound binomial model. Firstly, the risk model is set in the framework of PDMP, and the extended generator technique of PDMP is applied to the continuous-time risk model, then an （impulse） integral-differential equation for the expected value is derived, and a recursive equation for the ruin probability is obtained.