A Hybrid Estimate for the Finite-time Ruin Probability in a Bivariate Autoregressive Risk Model with Application to Portfolio Optimization

Consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another autoregressive process, independent of the former one. We derive an asymptotic formula for the finite-time ruin probability and propose a hybrid method, combining simulation with asymptotics, to compute this ruin probability more effi ciently. As an application, we consider a portfolio optimization problem in which we determine the proportion invested in the risky stock that maximizes the expected terminal wealth subject to a constraint on the ruin probability.