Uniform asymptotics for a time-dependent bidimensional delay-claim risk model with stochastic return and dependent subexponential claims

In this paper, we consider a bidimensional risk model with stochastic returns and dependent subexponential claims, in which every main claim may be accompanied by a delayed claim, occurring after an uncertain period of time. The surplus of each business line is allowed to be invested in a portfolio of risk-free assets, and the price process of the investment is modeled by a geometric Lévy process. Meanwhile, we employ a time-claim-dependent structure to describe the dependence among claims and the interarrival times. Some uniform asymptotic formulas for the finite-time ruin probabilities are derived under this structure. Finally, a simulation study is conducted to evaluate the accuracy of the derived results.