## 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.

Original language | English (US) |
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Pages (from-to) | 378-397 |

Number of pages | 20 |

Journal | North American Actuarial Journal |

Volume | 16 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1 2012 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty