Approximations for finite-time ruin probability in a dependent discrete-time risk model with CMC simulations

Consider a discrete-time risk model in which the insurer is allowed to invest its wealth into a risk-free or a risky portfolio under a certain regulation. Then the insurer is said to be exposed to a stochastic economic environment that contains two kinds of risks, the insurance risk and financial risk. Within period i, the net insurance loss is denoted by Xi and the stochastic discount factor from time i to zero is denoted by θi. For any integer n, assume that X1,…,Xn form a sequence of pairwise asymptotically independent but not necessarily identically distributed real-valued random variables with distributions F1,…,Fn, respectively; θ1,θ2,…,θn are another sequence of arbitrarily dependent positive random variables; and the two sequences are mutually independent. Under the assumption that the average distribution n−1∑i=1nFi is dominatedly varying tailed and some moment conditions on θi,i=1,…,n, we derive a weakly equivalent formula for the finite-time ruin probability. We demonstrate our obtained results through a Crude Monte-Carlo simulation with asymptotics.