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

• This paper considers a multidimensional risk model with an investment return process modelled by a general càdlàg process. • The claim sizes from different lines of business are distributed according to the multivariate regular variation. • Conditions are proposed that can guarantee the uniformity of three types of ruin probabilities for the entire time horizon. • The conditions proposed are weak enough to be satisfied by some stochastic processes, such as the Lévy process, Vasicek model, Cox-Ingersoll-Ross model, Heston model, and Stochastic volatility model. 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. [ABSTRACT FROM AUTHOR]