Estimations For The Ruin Probability Of Insurance Risk Models With Financial Risks

In finance and insurance,the estimation and prevention of risk is an important problem.The ruin probability can characterize the risk of insurance business well.This paper mainly discusses the ruin probability of the insurance risk model with financial risk,and focuses on the following three questions.Firstly,in order to prepare for the estimation of the ruin probability of the risk model,this paper discusses the precise large deviations for the partial sums of the widely orthant dependent random variables with different distributions.Compared with the existing results,under some conditions which are easier to verify,we get the upper and lower bounds of the precise large deviations for the partial sums of the dependent random variables.Secondly,in the discrete-time risk model with financial risk,when there is a bivariate Sarmanov distribution between the financial and insurance risks,and the insurance risks have a light-tailed distribution,the asymptotic estimation of the ruin probability of the above risk model is discussed.Thirdly,in the continuous-time risk model with financial risk,the paper discusses the situation of stochastic investment return,and focuses on the case that the price process of the investment portfolio is a geometric Lévy process.For the case that the claims have subexponential distributions,we discuss the finite-time ruin probability of the above risk model.We further verify the perturbation of the heavy-tailed claims risk model has no effect on the ruin probability.