二维风险模型中Copula 相依下的破产概率

在本文中, 我们把Copula 连结函数用到二维的风险模型中, 考虑两个模型索赔额之间基于Copula 的相依关系. 首先对二维复合Poisson 模型给出了最早破产时刻定义下的生存概率满足的偏微分方程; 然后对二维的复合二项模型, 分别在连续型索赔额分布和离散型索赔额分布下给出了不同定义的生存概率和破产概率的递归公式, 并且特别选择了FGM Copula 连结函数, 给出了相应的结果; 另外在离散型分布下, 对于其Copula 函数的不唯一性进行了说明.

The ruin probabilities for the two-dimensional risk model based on Copula dependence

During the process of applying the Copulas in the two-dimensional risk models, with the consideration of the dependence relation between the claim amounts, the author chooses the FGM Copula to be put into application. For the compound Poisson model, a partial integro-differential equation satisfied by the survival probability is derived. The recursive formula of the finite-time survival or ruin probabilities are then derived separately in the situation of continuous and discrete distribution of claim amount, for the compound binomial model. Furthermore, the uncertainty for the Copulas under the discrete case is also illustrated.