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Optimal prevention strategies in the classical risk model

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 first risk model in which the insurer may invest into a prevention plan which decreases claim intensity. We determine the optimal prevention investment for different risk indicators. In particular, we show that the prevention amount minimizing the ruin probability maximizes the adjustment coefficient in the classical ruin model with prevention, as well as the expected dividends until ruin in the model with dividends. We also show that the optimal prevention strategy is different if one aims at maximizing the average surplus at a fixed time horizon. A sensitivity analysis is carried out. We also prove that our results can be extended to the case where prevention starts to work only after a minimum prevention level threshold.

Suggested Citation

  • Romain Gauchon & Stéphane Loisel & Jean-Louis Rullière & Julien Trufin, 2020. "Optimal prevention strategies in the classical risk model," Post-Print hal-02314899, HAL.
    • Handle: RePEc:hal:journl:hal-02314899
    Note: View the original document on HAL open archive server: https://hal.science/hal-02314899v2
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    References listed on IDEAS

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    1. Dionne, Georges & Eeckhoudt, Louis, 1985. "Self-insurance, self-protection and increased risk aversion," Economics Letters, Elsevier, vol. 17(1-2), pages 39-42.
    2. Ehrlich, Isaac & Becker, Gary S, 1972. "Market Insurance, Self-Insurance, and Self-Protection," Journal of Political Economy, University of Chicago Press, vol. 80(4), pages 623-648, July-Aug..
    3. Hojgaard, Bjarne & Taksar, Michael, 1998. "Optimal proportional reinsurance policies for diffusion models with transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 41-51, May.
    4. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    5. Afonso, Lourdes B. & Reis, Alfredo D. Egídio dos & Waters, Howard R., 2010. "Numerical Evaluation of Continuous Time Ruin Probabilities for a Portfolio with Credibility Updated Premiums," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 399-414, May.
    6. 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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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Prevention; Optimal prevention strategy; Ruin theory; Insurance;
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