Analysis On Ruin Probability Of Dependent Risk Model

Ruin theory is one of the core contents of insurance risk theory.Predicting the ruin probability in a limited or infinite time can help an insurance company better check its solvency and control the risk of its financial business.However,with the global development of the insurance company’s business and economy,the classical risk model can no longer meet the business needs of the insurance company,It is necessary to consider the influence of interest rate and other random factorsBased on the dependence of insurance risk and financial risk,this paper studies the asymptotic representation of ruin probability of discrete-time model,and our core problem is to analyze the tail characteristics of the product of insurance risk variable X and financial risk variable Y.Therefore,Under the assumption that X and Y satisfy certain dependent structure,and that F of X belongs to the family of regular variable tail distribution,we first prove that the distribution of the product of Xand Y belongs to the family of regular variable tail distribution.Then,the above results are combined with Breiman’s theorem under the dependent structure to apply to the dependent risk model,and the asymptotic representation of ruin probability in finite time is obtained when the insurance risk belongs to the family of regular change tail distribution.