Asymptotic estimates for finite-time ruin probability in a discrete-time risk model with dependence structures and CMC simulations

Abstract

Consider a discrete-time risk model with dependence structures, where claim sizes are assumed to follow a one-sided linear process whose innovations further obey a so-called bivariate upper tail independence. The stochastic discount factors follow a stationary causal process. Then, the insurer is said to be exposed to a stochastic economic environment that contains two kinds of risks, i.e. the insurance risk and financial risk. The two kinds of risks form a sequence of independent and identically distributed random pairs which are copies of a random pair with a common bivariate Sarmanov dependent distribution. When the distributions of the innovations belong to the intersection of the dominated-variation class and the long-tailed class, we derive some asymptotic formulas for the finite-time ruin probability. We also get conservative asymptotic bounds when the distributions of the innovations belong to the regular variation class. Finally, we verify our results through a Crude Monte Carlo simulation.