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On Optimal Cancellation of Policies

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  • Gerber, Hans U.

Abstract

One of the basic problems in life is: Given information (from the past), make decisions (that will affect the future). One of the classical actuarial examples is the adaptive ratemaking (or credibility) procedures; here the premium of a given risk is sequentially adjusted, taking into account the claims experience available when the decisions are made.In some cases, the rates are fixed and the premiums cannot be adjusted. Then the actuary faces the question: Should a given risk be underwritten in the first place, and if yes, what is the criterion (in terms of claims performance) for cancellation of the policy at a later time?Recently, Cozzolino and Freifelder [6] developed a model in an attempt to answer these questions. They assumed a discrete time, finite horizon, Poisson model. While the results lend themselves to straightforward numerical evaluation, their analytical form is not too attractive. Here we shall present a continuous time, infinite horizon, diffusion model. At the expense of being somewhat less realistic, this model is very appealing from an analytical point of view.Mathematically, the cancellation of policies amounts to an optimal stopping problem, see [8], [4], or chapter 13 in [7], and (more generally) should be viewed within the framework of discounted dynamic programming [1], [2].

Suggested Citation

  • Gerber, Hans U., 1977. "On Optimal Cancellation of Policies," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 125-138, January.
    • Handle: RePEc:cup:astinb:v:9:y:1977:i:1-2:p:125-138_01
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    Cited by:

    1. Szölgyenyi Michaela, 2015. "Dividend maximization in a hidden Markov switching model," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 143-158, December.
    2. Michaela Szolgyenyi, 2016. "Dividend maximization in a hidden Markov switching model," Papers 1602.04656, arXiv.org.
    3. Gunther Leobacher & Michaela Szolgyenyi & Stefan Thonhauser, 2016. "Bayesian Dividend Optimization and Finite Time Ruin Probabilities," Papers 1602.04660, arXiv.org.
    4. Bjarne Højgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 315-327.
    5. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    6. Cohen, Albert, 2010. "Examples of optimal prediction in the infinite horizon case," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 950-957, June.
    7. Albert Cohen, 2018. "Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance," Risks, MDPI, vol. 6(1), pages 1-3, January.

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