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

Olivier Lopez () and Daniel Nkameni ()
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Olivier Lopez: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique, IP Paris - Institut Polytechnique de Paris
Daniel Nkameni: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique, IP Paris - Institut Polytechnique de Paris

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Abstract: In this paper, we address the problem of providing insurance protection against heavy-tailed losses for which the expected loss may not even be finite. The product we study combines traditional insurance coverage up to a given limit with parametric (or index-based) coverage for larger losses. This second component is computed using covariates available immediately after a loss occurs, thereby reducing claims management costs through rapid compensation. To optimize its design, we use a criterion tailored to extreme losses, that is, to Pareto-type loss distributions. We support the calibration procedure with theoretical results establishing its convergence rate, as well as empirical evidence from both a simulation study and a real-data analysis of tornado losses in the United States. We also propose a two-step optimization procedure as a potential solution to the scarcity of data in the tails of loss distributions. Finally, we empirically demonstrate that the proposed hybrid contract outperforms a traditional capped indemnity contract.

Keywords: Parametric insurance; Heavy-tailed distributions; Natural disasters; Capped indemnity contracts; Contrat indemnitaire plafonné; Catastrophes naturelles; Distributions à queue lourde; Assurance paramétrique (search for similar items in EconPapers)
Date: 2025-07-08
Note: View the original document on HAL open archive server: https://hal.science/hal-04959706v5
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