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 X-i and the stochastic discount factor from time i to zero is denoted by theta(i). For any integer n, assume that X-1,...,X-n form a sequence of pairwise asymptotically independent but not necessarily identically distributed real-valued random variables with distributions F-1,...,F-n, respectively; theta(1),theta(2),...,theta(n) On 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)Sigma F-n(i=1)i is dominatedly varying tailed and some moment conditions on theta(i,)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. (C) 2017 Elsevier B.V. All rights reserved.