Limani, Jeta and Bettinger, Régis and Dacorogna, Michel M
(2017):
*On the diversification benefit of reinsurance portfolios.*

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## Abstract

In this paper we compare the diversification benefit of portfolios containing excess-of-loss treaties and portfolios containing quota-share treaties, when the risk measure is the (excess) Value-at-Risk or the (excess) Expected Shortfall. In a first section we introduce the set-up under which we perform our investigations. Then we show that when the losses are continuous, independent, bounded, the cover unlimited and when the risk measure is the Expected Shortfall at a level alpha close to 1, a portfolio of n excess-of-loss treaties diversifies better than a comparable portfolio of n quota-share treaties. This result extends to the other risk measures under additional assumptions. We further provide evidence that the boundedness assumption is not crucial by deriving analytical formulas in the case of treaties with i.i.d. exponentially distributed original losses. Finally we perform the comparison in the more general setting of arbitrary continuous joint loss distributions and observe in that case that a finite cover leads to opposite results, i.e. a portfolio of n quota-share treaties diversifies better than a comparable portfolio of n excess-of-loss treaties at high quantile levels.

Item Type: | MPRA Paper |
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Original Title: | On the diversification benefit of reinsurance portfolios |

Language: | English |

Keywords: | Diversification benefit, risk measures, portfolio, excess-of-loss treaties |

Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C00 - General C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General |

Item ID: | 82466 |

Depositing User: | Dr Michel M Dacorogna |

Date Deposited: | 12 Nov 2017 20:15 |

Last Modified: | 06 Oct 2019 10:24 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/82466 |