Ruin Probability for a Two-Dimensional Perturbed Risk Model with Thinning Dependence and Stochastic Premiums

This mansuscript focuses on a kind of two-dimensional risk model with stochastic premium income and the model allows for dependence between premiums and claims. By Laplace transforms, we prove that the model proposed in this paper can be reduced into a kind of risk model with stochastic premium incomes, and the premium income is independent of the claim process. When the individual claims are the "light-tailed" case, an upper bound for ruin probability is derived by martingale approach. When the claims belong to a kind of heavy-tailed distribution, the asymptotic estimation for ruin probability is given when the initial surplus tends to infinity.