Uniform asymptotics for ruin probabilities of multidimensional risk models with stochastic returns and regular variation claims

Abstract

Consider a multidimensional discrete-time risk model in terms of some dependence structure. For the case of multivariate regularly varying claims, we study the asymptotic behavior of the ruin probabilities determined by some ruin sets. The estimates hold uniformly for all time horizons. Then we focus on a ruin set that allows partial capital transfers. As an application, the optimal allocation of the initial reserve is obtained. Some numerical simulations are presented to illustrate the results.