Uniform asymptotic estimates in a time-dependent risk model with general investment returns and multivariate regularly varying claims

Abstract

Consider an insurer with d lines of business and the freedom to make risk-free and risky investments. The investment portfolio price process is described as a general càdlàg process. It is assumed that the claim sizes from different lines of business and their common inter-arrival times form a sequence of independent and identically distributed (i.i.d.) random pairs, each pair obeying a particular dependence structure. With this dependence structure, claim sizes from different lines of business are distributed according to the multivariate regular variation. This paper proposes conditions that can be satisfied by several important stochastic processes, including the Lévy process, Vasicek interest rate model, Cox-Ingersoll-Ross interest rate model, Heston model, and Stochastic volatility model. Under these conditions, the uniform asymptotic expansions of ruin probabilities are derived, which hold uniformly for the entire time horizon. Numerical examples are provided as a means of illustrating the main results.