Asymptotic analysis of tail moment in a dependent risk model

In this paper, we discuss a risk model with multiple business lines, where the log-discount process is a combination of a general adapted process with continuous paths and a compound stochastic jump process. We propose a dependence structure under the framework of multivariate regular variation, which not only captures the dependence among the insurance losses but also the one between the insurance losses and the financial jump sizes. We study a novel tail moment risk measure defined as the conditional moment of the present value of an individual business line's aggregate losses, given that the present value of aggregate losses of all business lines exceeds its Value-at-Risk. With the help of Extreme Value Theory, we derive asymptotic expansion of the tail moment. We illustrate the main results with some numerical studies which reveal that while the tail moment is notably impacted by the dependence structure, the heavy-tailedness plays a comparatively more significant role.