Estimation Of Ruin Probability In Bidimensional Dependent Risk Model

Bankruptcy theory is one of the hot topics in risk theory.Ruin probability is one of the important indexes to measure the robustness of insurance companies.This paper discusses the one-dimensional risk model and two-dimensional risk model.For one-dimensional risk model,geometric Lévy process is used to describe the price process of portfolio.This paper mainly discusses inter-arrival times which are independent of claim sizes and which are independent and identically distributed random variables.When claim sizes have upper tail asymptotically independent dependent structure and their distributions belong to the class D ,the asymptotic estimation of the finite ruin probability is obtained.When claim sizes have negative quadrant dependent structure and their distributions belong to the class C,the asymptotic estimation of the tail of the discounted aggregate claims is obtained.In the two-dimensional risk model,the paper considers the case that counting processes of two kinds of business of insurance company are arbitrarily dependent,and claim sizes of two kinds of business have respectively conditional independent dependent structure.When their distributions belong to the class (?),the asymptotic estimation of infinite time ruin probability is obtained.When their distributions belong to the class ,the asymptotic estimation of the finite time ruin probability is obtained with a Brownian perturbation.