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

Qihe Tang and Zhongyi Yuan

North American Actuarial Journal, 2012, vol. 16, issue 3, 378-397

Abstract: 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 auto regressive 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 efficiently. 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.

Date: 2012
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DOI: 10.1080/10920277.2012.10590648

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