Second-order asymptotic for aggregate losses in a discrete-time risk model with multivariate interdependent insurance and financial risks

This paper investigates the second-order asymptotic tail behavior of stochastic discounted aggregate losses in a discrete-time model, capturing the multidimensional dependence between insurance and financial risks via a multivariate Farlie-Gumbel-Morgenstern distribution. Moving beyond the restrictive assumption of independence or bivariate dependence prevalent in the literature, we derive a second-order asymptotic approximation for the tail probability under the general condition that insurance risks possess a second-order subexponential tail. Our main result provides a closed-form expression that explicitly quantifies the impact of inter-risk dependencies, significantly refining the conventional first-order asymptotics. Simulation studies confirm that the proposed second-order formula markedly enhances estimation accuracy, offering a more reliable tool for capital allocation and risk management.