Second-order asymptotics for randomly weighted sums of dependent subexponential random variables with applications to insurance

In this paper, we derive a second-order asymptotic formula for the tail probability of a randomly weighted sum, where the primary random variables follow second-order subexponential distributions and exhibit a multivariate Farlie-Gumbel-Morgenstern dependence structure. This result significantly improves existing first-order asymptotic results. Simulation studies are conducted to assess the accuracy of our asymptotic formula, demonstrating its improvement over first-order counterparts. As an application, we investigate a nonstandard continuous-time risk model with a constant force of interest and establish the second-order asymptotics of the discounted aggregate claims.