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Quantile Mixing and Model Uncertainty Measures


  • Thierry Cohignac
  • Nabil Kazi-Tani

    () (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)


In this paper, we introduce a new simple methodology for combining two models, which are given in the form of two probability distributions. We use convex combinations of quantile functions, with weights depending on the quantile level. We choose the weights by comparing, for each quantile level, a given measure of model uncertainty calculated for the two probability distributions that we want to combine. This methodology is particularly useful in insurance and reinsurance of natural disasters, for which there are various physical models available, along with historical data. We apply our procedure to a real portfolio of insurance losses, and show that the model uncertainty measures have a similar behavior on the set of various insurance losses that we consider. This article serves also as an introduction to the use of model uncertainty measures in actuarial practice.

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  • Thierry Cohignac & Nabil Kazi-Tani, 2019. "Quantile Mixing and Model Uncertainty Measures," Working Papers hal-02405859, HAL.
  • Handle: RePEc:hal:wpaper:hal-02405859
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    References listed on IDEAS

    1. Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005. "Subadditivity Re–Examined: the Case for Value-at-Risk," FMG Discussion Papers dp549, Financial Markets Group.
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    5. Graham Elliott & Allan Timmermann, 2016. "Economic Forecasting," Economics Books, Princeton University Press, edition 1, number 10740.
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    7. 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.
    8. N/A, 2016. "The World Economy: Forecast Summary," National Institute Economic Review, National Institute of Economic and Social Research, vol. 238(1), pages 2-2, November.
    9. N/A, 2016. "The UK Economy: Forecast summary," National Institute Economic Review, National Institute of Economic and Social Research, vol. 237(1), pages 3-3, August.
    10. Barrieu, Pauline & Scandolo, Giacomo, 2015. "Assessing financial model risk," European Journal of Operational Research, Elsevier, vol. 242(2), pages 546-556.
    11. Zhaoxu Hou & Jan Obłój, 2018. "Robust pricing–hedging dualities in continuous time," Finance and Stochastics, Springer, vol. 22(3), pages 511-567, July.
    12. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
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    More about this item


    Model combination; Model uncertainty; Quantiles; Risk management; Catastrophe models;
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