带投资和退保的离散时间风险模型的破产概率

Ruin Probability for Discrete Time Risk Model with Investment and Surrender

为了对投资和退保等随机性的风险进行控制和研究,并探究索赔相依关系对保险公司的破产的影响程度,分别在索赔相依和索赔独立时建立带投资和退保的离散时间风险模型并进行对比;在索赔相依时假设每次主索赔可能引起2类副索赔之一,在索赔独立时假设可能发生3类相互独立的索赔;通过递推法得出2类模型中相应随机变量的数字特征,并运用强马尔科夫性推导其调节系数和破产概率的显性表达式;结合一个具体数例对比研究2类模型的破产概率,并分析索赔概率、退保率等特征参数对相依索赔风险模型的破产概率的影响。结果表明,相依性增大了风险模型的破产概率,并且不同保险公司对风险模型的破产概率的要求可通过适当调整各特征参数而实现。

To control and study the risk of randomness such as investment and surrender, and explain the influence extent of correlated-claims relationship on the insolvency of the insurance company, the discrete time risk models with investment and surrender were established respectively under correlated claims and independent claims conditions to contrast. In the correlated-claims risk model, it was assumed that each of the main claims might cause one of the two types of by-claims. In the independent-claims risk model, it was assumed that there might occur three types of mutually independent claims. By using the recursive method, the numerical characteristics of the random variables in the two types of models were derived. By using strong Markov property, the explicit expressions of the adjustment coefficients and ruin probabilities of the two types of models were obtained. A numerical example was presented to compare the ruin probabilities of these two models, and the effects of characteristic parameters such as claim probability and surrender rate on the ruin probability of the correlated claim risk model were analyzed. The results show that the dependence increases the ruin probability of the risk model, and the requirements of different insurance companies for the ruin probability of the risk model can be satisfied by appropriately adjusting the characteristic parameters.