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Solvency tuned premium for a composite loss distribution

Author

Listed:
  • Alexandre Brouste

    (LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université)

  • Anis Matoussi

    (Département de Mathématiques [Le Mans] - UM - Le Mans Université)

  • Tom Rohmer

    (LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université)

  • Christophe Dutang

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

  • Vanessa Désert

    (IRA - Institut du Risque et de l'Assurance, Le Mans, MMA - Mutuelles du Mans Assurances)

  • Erwan Gales

    (MMA - Mutuelles du Mans Assurances)

  • Pierre Golhen

    (MMA - Mutuelles du Mans Assurances)

  • Bérengère Milleville

    (MMA - Mutuelles du Mans Assurances)

  • Willie Lekeufack

    (MMA - Mutuelles du Mans Assurances, ISFA - Institut de Science Financière et d'Assurances)

Abstract

A parametric framework is proposed to model both attritional and atypical claims for insurance pricing. This model relies on a classical Generalized Linear Model for attritional claims and a non-standard Generalized Pareto distribution regression model for atypical claims. Maximum likelihood estimators (closed-form for the Generalized Linear Model part and computed with Iterated Weighted Least Square procedure for the Generalized Pareto distribution regression part) are proposed to calibrate the model. Two premium principles (expected value principle and standard deviation principle) are computed on a real data set of fire warranty of a corporate line-of-business. In our methodology, the tuning of the safety loading in the two premium principles is performed to meet a solvency constraint so that the premium caps a high-level quantile of the aggregate annual claim distribution over a reference portfolio.

Suggested Citation

  • Alexandre Brouste & Anis Matoussi & Tom Rohmer & Christophe Dutang & Vanessa Désert & Erwan Gales & Pierre Golhen & Bérengère Milleville & Willie Lekeufack, 2018. "Solvency tuned premium for a composite loss distribution," Working Papers hal-01883508, HAL.
    • Handle: RePEc:hal:wpaper:hal-01883508
    Note: View the original document on HAL open archive server: https://hal.science/hal-01883508
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    Keywords

    commercial lines; non-life insurance; pricing; composite distribution; solvency criterion;
    All these keywords.

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