Asymptotics For The Finite-time Ruin Probabilities Of A Two-dimensional Risk Model

This paper mainly concerns asymptotic behaviour for the finite-time ruin proba-bilities of a two-dimensional dependence risk model under subexponential claim sizes. Based on standard renewal risk model (i.e. Sparre Andersen model), we consider the two-dimensional dependence risk model because of the assumption that the two risk pro-cesses have some common claim times. According to the definitions of ruin times for the two-dimensional risk model, the main focus is three types of finite-time ruin probabilities. We extent the problem that the single risk process goes below0in the finite time to the following three problems:both of the risk processes go below0in the finite time, at least one of the processes goes below0in the finite time and the maximum of the two risk pro-cesses goes below0in the finite time. For each problem, the asymptotic formulas which hold uniformly in the corresponding regions are given.