## Abstract

Assume that an insurance company pays dividends to its shareholders whenever the surplus process is above a given threshold. In this paper we study the expected amount of dividends paid, and the expected time to ruin in the compound Poisson risk process perturbed by a Brownian motion. Two models are considered: In the first one the insurance company pays whatever amount exceeds a given level b as dividends to its shareholders. In the second model, the company starts to pay dividends at a given rate, smaller than the premium rate, whenever the surplus up-crosses the level b. The dividends are paid until the surplus down-crosses the level a, a < b. We assume that the claim sizes are phase-type distributed. In the analysis we apply the multidimensional Wald martingale, and the multidimensional Asmussesn and Kella martingale.

Original language | English |
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Pages (from-to) | 183-206 |

Number of pages | 24 |

Journal | ASTIN Bulletin |

Volume | 38 |

Issue number | 1 |

DOIs | |

State | Published - May 2008 |

## Keywords

- Kella and Whitt martingale
- Optional sampling theorem
- Stopping time
- Wald martingale

## ASJC Scopus subject areas

- Accounting
- Finance
- Economics and Econometrics