索赔到达间隔为几何分布风险模型的破产问题

Ruin probability of risk model with inter-occurrence of geometric distribution

讨论了索赔到达间隔时间服从几何分布,索赔额分布为一般离散型分布的一类连续时间风险模型的破产问题,先将风险模型纳入PDMP框架,借助于带离散分量的广义生成元的概念得到相关鞅,再利用测度变换理论得到破产概率的一般表达式,有趣的是破产函数不是连续的,而是逐段常值的.

The paper discusses the ruin problem of a kind of continuous-time risk model with inter-occurrence time obeyed geometric distribution and with claim size obeyed general discrete distribution. Firstly, we set the risk model in the framework of PDMP, and get a correlative martingale in virtue of the extended generator with discrete component. Secondly, the general expressions for ruin probabilities are presented via the change of the probability measure. It is interesting that the ruin probability function is not continuous, in fact, it is piecewise constant.