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Quantile Mixing and Model Uncertainty Measures

Author

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  • Thierry Cohignac
  • Nabil Kazi-Tani

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

Abstract

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.

Suggested Citation

  • Thierry Cohignac & Nabil Kazi-Tani, 2019. "Quantile Mixing and Model Uncertainty Measures," Working Papers hal-02405859, HAL.
  • Handle: RePEc:hal:wpaper:hal-02405859
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-02405859
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    References listed on IDEAS

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    Keywords

    Model combination; Model uncertainty; Quantiles; Risk management; Catastrophe models;
    All these keywords.

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