Uniform asymptotics for ruin probabilities in a two-dimensional nonstandard renewal risk model with stochastic returns

Dingcheng Wang,Yinghua Dong

doi:10.1186/s13660-018-1913-6

Abstract

In this paper, we consider a two-dimensional nonstandard renewal risk model with stochastic returns, in which the two lines of claim sizes form a sequence of independent and identically distributed random vectors following a bivariate Sarmanov distribution, and the two claim-number processes satisfy a certain dependence structure. When the two marginal distributions of the claim-size vector belong to the intersection of the dominated-variation class and the class of long-tailed distributions, we obtain uniform asymptotic formulas of finite-time and infinite-time ruin probabilities.

Highlights

In this paper, we study a two-dimensional nonstandard renewal risk model with stochastic returns, in which an insurer simultaneously operates two kinds of insurance businesses
When the marginal distributions of the claim-size vector belong to the regular variation class, the above reference presented uniform asymptotic formulas for the finite-time ruin probability
Fu and Ng [11] discussed a two-dimensional renewal risk model, in which there is a FGM structure between the claim sizes from two different lines of businesses, and showed uniform asymptotic formulas of the finite-time ruin probability, when the distributions of claim sizes belong to the intersection of the dominated varying class and the class of long-tailed distributions

Summary

Introduction

We study a two-dimensional nonstandard renewal risk model with stochastic returns, in which an insurer simultaneously operates two kinds of insurance businesses. When the marginal distributions of the claim-size vector belong to the regular variation class, the above reference presented uniform asymptotic formulas for the finite-time ruin probability.

Results

Conclusion