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An adaptive premium policy with a Bayesian motivation in the classical risk model

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  • Landriault, David
  • Lemieux, Christiane
  • Willmot, Gordon E.

Abstract

In this paper, we consider an extension of the classical risk model in which the premium rate policy is adaptive to claim experience. We assume that the premium rate is reviewed each time the surplus reaches a new descending ladder height. A choice between a finite number m of rates is then made depending on the time elapsed between successive ladder heights. We derive explicit expressions for the probability of ruin in this model, assuming claim sizes have a mixed Erlang distribution. We then motivate further the idea behind this adaptive premium rate policy by using a mixed Poisson process for the claim arrival, and propose a method to fix the parameters of the policy in this setting. Finally, we discuss other applications of this method.

Suggested Citation

  • Landriault, David & Lemieux, Christiane & Willmot, Gordon E., 2012. "An adaptive premium policy with a Bayesian motivation in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 370-378.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:370-378
    DOI: 10.1016/j.insmatheco.2012.06.001
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    Cited by:

    1. G. A. Delsing & M. R. H. Mandjes & P. J. C. Spreij & E. M. M. Winands, 2018. "An optimization approach to adaptive multi-dimensional capital management," Papers 1812.08435, arXiv.org.
    2. Guelman, Leo & Guillén, Montserrat & Pérez-Marín, Ana M., 2014. "A survey of personalized treatment models for pricing strategies in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 68-76.
    3. Delsing, G.A. & Mandjes, M.R.H. & Spreij, P.J.C. & Winands, E.M.M., 2019. "An optimization approach to adaptive multi-dimensional capital management," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 87-97.
    4. Li, Shu & Landriault, David & Lemieux, Christiane, 2015. "A risk model with varying premiums: Its risk management implications," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 38-46.

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    More about this item

    Keywords

    Ruin probability; Mixed Erlang; Defective renewal equation; Laplace transform; Erlangization; Mixed Poisson; IM10; IM13; IM30;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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