Some Asymptotic Results Of The Ruin Probabilities In A Bidimensional Renewal Risk Model With Brownian Perturbation

The study of ruin probability has a profound significance in insurance and actuarial science.It is difficult to get the value of ruin probability.Hence,the asymptotic study of ruin probability is important.Up until now,the asymptotic behavior of finite-time ruin probabilities for onedimensional or two-dimensional risk models with heavy-tailed claims has been studied by quite a few researchers.And they had a lot of inspiring results.With the study of risk models,researchers at home and abroad began to promote the classical model.In this paper,the asymptotic behaviour for the finite-time ruin probabilities of a bidimensional renewal risk model with constant force of interest and Brownian perturbation is mainly concerned.Compared to previous studies,N(t)is a renewal claim-number process that does not exist extra constraints and the claim-size distribution function is from the subexponential class.First,we give three types of ruin probability: both of the surplus processes go below 0in the finite time?the maximum of the two surplus processes goes blow 0 in the finite time?at least one of the surplus processes goes below 0 in the finite time.This paper considers two models: In one of the models,two classes of claims share the same arrival times,while in the another model,two classes of claims have difficult arrival times.For each problem,three types of the finite-time ruin probabilities under this model are discussed.We obtain the asymptotic formulas for the three types,which hold uniformly for any finite time horizon.Besides,asymptotic results confirm that bidimensional risk models with heavy-tailed claims are insensitive to the Brownian perturbation.