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A hybrid estimate for the finite-time ruin probability in a bivariate autoregressive risk model with application to portfolio optimization. (English) Zbl 1291.91128

Summary: 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91G10 Portfolio theory
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