索赔稀疏两维风险模型的破产问题
发布时间：2018-11-10 16:29
【摘要】：随着保险业的快速发展,保险公司经营规模不断扩大,险种也趋于多样化和相依化,只考虑含有一种险种的风险模型已经不能满足保险公司的风险管理需求,因此需要将多个险种联合起来,综合考虑保险公司的风险情况,而保险公司的险种的索赔次数之间往往又具有某种相关性,因此结合保险公司实际运营,对相依的多险种模型的破产问题进行研究,无论对保险公司经营,还是对监督部门的监管,都具有十分重要的意义。 为此,考虑一种稀疏相依的双险种风险模型：假定N1(t)=N11(t)+N21(t),N2(t)=N22(t)+N12(t),{N11(t),t0}为参数为λ11的Poisson过程,相应的{N12(t),t0}是{N11(t),t0}的一个p1-稀疏过程,{N22(t),t0}是参数为λ22的Poisson过程,相应的{N21(t),t0}是{N22(t),t0}的一个p2-稀疏过程,Poisson过程{N22(t),t0}与{N11(t),t0}相互独立。首先,将两个模型结合成一个模型,建立了索赔次数稀疏相依的风险模型,对模型破产概论进行了研究,同时讨论了稀疏性强弱对保费收取以及破产概论的影响；其次,将模型视为一个两维稀疏相依的风险模型,得出了生存概率满足的偏积分微分方程,并且就指数分布条件之下,给出了计算生存概率的一个迭代算法。
[Abstract]:With the rapid development of insurance industry, the scale of insurance companies is expanding and the types of insurance are becoming diversified and dependent. Considering only one kind of insurance risk model can not meet the risk management needs of insurance companies. Therefore, it is necessary to combine multiple types of insurance to consider the risk situation of the insurance company, and the number of claims of the insurance company is often related to each other. Therefore, combined with the actual operation of the insurance company, It is of great significance to study the bankruptcy of the dependent multi-insurance model, not only to the management of insurance companies, but also to the supervision of supervision departments. For this reason, we consider a sparsely dependent risk model of double types of insurance: assume N1 (t) = N11 (t) N21 (t), N2 (t) = N22 (t) N12 (t), {N11 (t), t 0} as Poisson process with parameter 位 11, corresponding {N12 (t), T0} is a p1-sparse process of {N11 (t), t0}, {N22 (t), t0} is a Poisson process with a parameter 位 22, and the corresponding {N21 (t), t0} is a p2-sparse process of {N22 (t), t0}. The Poisson process {N 22 (t), t 0} and {N 11 (t), t 0} are independent of each other. Firstly, the two models are combined into one model, and the risk model of sparse dependence of claim number is established, and the general theory of ruin is studied, and the influence of sparsity on premium collection and ruin is also discussed. Secondly, the model is regarded as a two dimensional sparse dependent risk model, and the partial integro-differential equation of survival probability is obtained, and an iterative algorithm for calculating survival probability is given under the condition of exponential distribution.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F840.3
本文编号：2322961
[Abstract]:With the rapid development of insurance industry, the scale of insurance companies is expanding and the types of insurance are becoming diversified and dependent. Considering only one kind of insurance risk model can not meet the risk management needs of insurance companies. Therefore, it is necessary to combine multiple types of insurance to consider the risk situation of the insurance company, and the number of claims of the insurance company is often related to each other. Therefore, combined with the actual operation of the insurance company, It is of great significance to study the bankruptcy of the dependent multi-insurance model, not only to the management of insurance companies, but also to the supervision of supervision departments. For this reason, we consider a sparsely dependent risk model of double types of insurance: assume N1 (t) = N11 (t) N21 (t), N2 (t) = N22 (t) N12 (t), {N11 (t), t 0} as Poisson process with parameter 位 11, corresponding {N12 (t), T0} is a p1-sparse process of {N11 (t), t0}, {N22 (t), t0} is a Poisson process with a parameter 位 22, and the corresponding {N21 (t), t0} is a p2-sparse process of {N22 (t), t0}. The Poisson process {N 22 (t), t 0} and {N 11 (t), t 0} are independent of each other. Firstly, the two models are combined into one model, and the risk model of sparse dependence of claim number is established, and the general theory of ruin is studied, and the influence of sparsity on premium collection and ruin is also discussed. Secondly, the model is regarded as a two dimensional sparse dependent risk model, and the partial integro-differential equation of survival probability is obtained, and an iterative algorithm for calculating survival probability is given under the condition of exponential distribution.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F840.3
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