### Abstract

Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are used, both involving various model parameters. In the first model the claims are simply independent, while a certain dependence structure is assumed in the second model. A relatively simple rule of thumb is formulated for choosing the best approximation for either model. This approximation satisfies the aforementioned criterion. Finally, by comparing the two models, it is demonstrated that a small degree of dependence between the claims already has a substantial effect on the stop-loss premiums. The difference can run up to a factor 500.

Original language | English |
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Place of Publication | Enschede |

Publisher | University of Twente, Faculty of Mathematical Sciences |

Number of pages | 15 |

Publication status | Published - 2003 |

### Publication series

Name | Memorandum Faculty of Mathematical Sciences |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1695 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-62P05
- MSC-62E17

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## Cite this

Reijnen, R., Albers, W., & Kallenberg, W. C. M. (2003).

*Approximations for stop-loss reinsurance premiums*. (Memorandum Faculty of Mathematical Sciences; No. 1695). Enschede: University of Twente, Faculty of Mathematical Sciences.