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Combination of traditional and parametric insurance: calibration method based on the optimization of a criterion adapted to heavy tail losses
[Combinaison d'assurance traditionnelle et paramétrique : méthode de calibration basée sur l'optimisation d'un critère adapté aux pertes à queue lourde]

Author

Listed:
  • Olivier Lopez

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Daniel Nkameni

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we consider the question of providing insurance protection against heavy tail losses, where the expectation of the loss may not even be finite. The product we study is based on a combination of traditional insurance up to some limit, and a parametric (or index-based) cover for larger losses. This second part of the cover is computed from covariates available just after the claim, allowing to reduce the claim management costs via an instant compensation. To optimize the design of this second part of the product, we use a criterion which aims to reflect the preferences of the policyholder, and is adapted to extreme losses (that is distribution of the losses that are of Pareto type). We support the calibration procedure by theoretical results that show its convergence rate, and empirical results from a simulation study and a real data analysis on tornados in the US.

Suggested Citation

  • Olivier Lopez & Daniel Nkameni, 2025. "Combination of traditional and parametric insurance: calibration method based on the optimization of a criterion adapted to heavy tail losses [Combinaison d'assurance traditionnelle et paramétrique," Working Papers hal-04959706, HAL.
    • Handle: RePEc:hal:wpaper:hal-04959706
    Note: View the original document on HAL open archive server: https://hal.science/hal-04959706v1
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