The Problem Of Ruin For One Class Of Sparse Dependent Bivariate Risk Modes

With the continuous development of the insurance industry,the company’s scale of operation is becoming larger,and types of insurance tend to diversify and dependency.So the classic risk model, which considers only one risk,can not meet the actual needs of the insurance company market operators,and is not enough for studying risk behaviorof insurance company. It’s of more practical significance for the insurance company operating and regulatory authority’supervise to introduce multi correlated aggregate claims models to describe the actual situation of insurance company.The paper considers a class of bivariate risk model with correlated aggregate claims as follows: where N1(t)=N11(t)+N12(t), and N2(t)=N22(t)+N12’(t),{N11(t),t≥0},{Nn(t),t≥0}{N22(t),t>0} are three indepengdent counting processes,{N12’(t),t≥0} is a p-sparse process of {N12(t),t≥0}.Firstly, he paper consider the case that{N11(t),t≥0},{N12(t),t≥0},{N22(t),t≥0} are all Poisson processes. In this case we get the integral equation of survival probability, Lundberg inequality and Cramer-Lundberg approximate of ruin probability. And further we get the exact expression of ruin probability when claims follow the exponential distributions. In addition, we study how the dependency affects on the upper bound of ruin probability.Then the paper further discusses the case that{N11(t),t≥0},{N22(t),t≥0} are both Poisson processes and {N11(t),t≥0} is an Erlang(2) process. In this case, by introducing auxiliary model, we get integral equation of ruin probability and discuss the asymptotic property of ruin probability with renewal method. We also get the linear differential equations of ruin probability for the model and corresponding auxiliary model when claims follow the exponential distributions, and show how solves the linear differential equations by a specific example.