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Optimal prevention of large risks with two types of claims

Author

Listed:
  • Romain Gauchon

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

  • Stéphane Loisel

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

  • Jean-Louis Rullière

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

  • Julien Trufin

    (Département de mathématiques Université Libre de Bruxelles - ULB - Université libre de Bruxelles)

Abstract

In this paper, we propose and study a risk model with two types of claims in which the insurer may invest into a prevention plan which decreases the intensity of large claims without impacting the small claims. We identify a necessary and sufficient condition for insurers to use prevention if there is no surplus. If, in addition, the severity of large claims dominates that of small claims by the harmonic mean residual life (HMRL) order, insurers invest more in prevention in the presence of a surplus. Finally, we characterize the asymptotic optimal prevention strategy when the initial surplus tends to infinity in the two main cases where both claim types are light-tailed and where one of them is light-tailed and the other one is heavy-tailed.

Suggested Citation

  • Romain Gauchon & Stéphane Loisel & Jean-Louis Rullière & Julien Trufin, 2020. "Optimal prevention of large risks with two types of claims," Post-Print hal-02314914, HAL.
    • Handle: RePEc:hal:journl:hal-02314914
    Note: View the original document on HAL open archive server: https://hal.science/hal-02314914v2
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    References listed on IDEAS

    as
    1. Courbage, Christophe & Rey, Béatrice, 2012. "Optimal prevention and other risks in a two-period model," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 213-217.
    2. Gauchon, Romain & Loisel, Stéphane & Rullière, Jean-Louis & Trufin, Julien, 2020. "Optimal prevention strategies in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 202-208.
    3. Hofmann, Annette & Peter, Richard, 2015. "Multivariate prevention decisions: Safe today or sorry tomorrow?," Economics Letters, Elsevier, vol. 128(C), pages 51-53.
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    6. Christophe Courbage & Henri Loubergé & Richard Peter, 2017. "Optimal Prevention for Multiple Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 899-922, September.
    7. Gerber, Hans U. & Goovaerts, Marc J. & Kaas, Rob, 1987. "On the Probability and Severity of Ruin," ASTIN Bulletin, Cambridge University Press, vol. 17(2), pages 151-163, November.
    8. Christophe Courbage, 2001. "Self-Insurance, Self-Protection and Market Insurance within the Dual Theory of Choice," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 26(1), pages 43-56, June.
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    More about this item

    Keywords

    Ruin theory; Prevention; Optimal prevention strategy; Insurance;
    All these keywords.

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