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On the diversification benefit of reinsurance portfolios

Author

Listed:
  • Limani, Jeta
  • Bettinger, Régis
  • Dacorogna, Michel M

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.

Suggested Citation

  • Limani, Jeta & Bettinger, Régis & Dacorogna, Michel M, 2017. "On the diversification benefit of reinsurance portfolios," MPRA Paper 82466, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:82466
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    File URL: https://mpra.ub.uni-muenchen.de/82466/1/MPRA_paper_82466.pdf
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    References listed on IDEAS

    as
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    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    4. David Bradley & Ramesh Gupta, 2002. "On the Distribution of the Sum of n Non-Identically Distributed Uniform Random Variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 689-700, September.
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    More about this item

    Keywords

    Diversification benefit; risk measures; portfolio; excess-of-loss treaties;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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