Joint Tail Probability of Renewal Models of Dependent Heavy‐Tailed Random Variables With Applications to Systemic Risk Measures

Consider a non‐standard renewal risk model in which claims arrive in pairs and the stochastic discounting process is given by , where is a Lévy process. We are interested in the joint tail probability of and , the aggregate discounted claims along the respective lines . Assume that is a sequence of independent and identically distributed random pairs with generic pair . Further assume that follows a dependence structure encompassing both tail dependence and tail independence, and has regularly varying marginal tails. We derive asymptotic formulas for the joint tail probability of and . These results are then applied to evaluate two systemic risk measures. Finally, we conduct numerical studies to illustrate the theoretical findings.