带干扰的单险种多索赔情形风险模型的破产概率

Ruin Probability in the Single-multiple-type Risk Model with Interference

【目的】基于大病保险等险种,建立一类带干扰的单险种多索赔情形的风险模型,为保险公司的风险管理及险种开发提供参考。【方法】假设保单到达过程为Poisson过程,各情形索赔到达过程为保单到达过程的p-稀疏过程,首先证明了调节系数的存在唯一性,然后利用鞅的性质及全期望公式对破产概率进行了探讨。【结果】得到了该模型下破产概率的Lundberg不等式及表达式。【结论】所探讨的风险模型接近现实实例,并可进一步推广,对实际情形具有一定的指导作用。

[Purposes]Consider a risk model with one insurance business which involves multiple claim cases based on catastrophic illness insurance and other insurances. [Methods] Assume that the income counting process is Poisson process, and the claim counting processes are p-sparse processes of the income counting process. The existence and uniqueness of adjustment coefficient is proved first, the ruin probability is studied by using martingale properties and law of total expectation. [Findings] Lundberg inequality and the generalized expression of ruin probability are obtained under the assumed model. [Conclusions] The constructed risk model has a certain guiding role in the insurance company＇s risk management and insurance development.