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.
Keywords: Dominated-variation distributions; Ruin probabilities; Stochastic returns; Two-dimensional risk model; Uniform asymptotic formulas.