Asymptotic Behavior of Discounted Aggregate Claims in a Nonstandard Two-dimensional Risk Model with Dependent Claim Sizes

Abstract

In this article, we study a nonstandard bivariate renewal risk model with dependent claim sizes, where two kinds of claim sizes constitute a sequence of independent and identically distributed random vectors satisfying a certain dependence structure, two claim-number processes are not necessarily independent. When the marginal distributions of the random vectors belong to the intersection of the class of long-tailed distributions and the class of the dominated variation distributions, we obtain joint tail asymptotic formulas of discounted total claims. The result shows that the dependence between two kinds of claims has an effect on the joint asymptotic tail probability of discounted total claims.