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Optimal Dividend Payment in De Finetti Models: Survey and New Results and Strategies

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  • Christian Hipp

    (Karlsruhe Institute of Technology, D-51465 Bergisch Gladbach, Germany)

Abstract

We consider optimal dividend payment under the constraint that the with-dividend ruin probability does not exceed a given value α . This is done in most simple discrete De Finetti models. We characterize the value function V ( s , α ) for initial surplus s of this problem, characterize the corresponding optimal dividend strategies, and present an algorithm for its computation. In an earlier solution to this problem, a Hamilton-Jacobi-Bellman equation for V ( s , α ) can be found which leads to its representation as the limit of a monotone iteration scheme. However, this scheme is too complex for numerical computations. Here, we introduce the class of two-barrier dividend strategies with the following property: when dividends are paid above a barrier B , i.e., a dividend of size 1 is paid when reaching B + 1 from B , then we repeat this dividend payment until reaching a limit L for some 0 ≤ L ≤ B . For these strategies we obtain explicit formulas for ruin probabilities and present values of dividend payments, as well as simplifications of the above iteration scheme. The results of numerical experiments show that the values V ( s , α ) obtained in earlier work can be improved, they are suboptimal.

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  • Christian Hipp, 2020. "Optimal Dividend Payment in De Finetti Models: Survey and New Results and Strategies," Risks, MDPI, vol. 8(3), pages 1-27, September.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:96-:d:411896
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    References listed on IDEAS

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    1. Sotomayor, Luz R. & Cadenillas, Abel, 2011. "Classical and singular stochastic control for the optimal dividend policy when there is regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 344-354, May.
    2. Kulenko, Natalie & Schmidli, Hanspeter, 2008. "Optimal dividend strategies in a Cramér-Lundberg model with capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 270-278, October.
    3. Pablo Azcue & Nora Muler, 2005. "Optimal Reinsurance And Dividend Distribution Policies In The Cramér‐Lundberg Model," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 261-308, April.
    4. 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.
    5. Christian Hipp, 2018. "Company Value with Ruin Constraint in a Discrete Model," Risks, MDPI, vol. 6(1), pages 1-14, January.
    6. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
    7. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2010. "An elementary approach to discrete models of dividend strategies," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 109-116, February.
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    Cited by:

    1. Katia Colaneri & Julia Eisenberg & Benedetta Salterini, 2022. "Some Optimisation Problems in Insurance with a Terminal Distribution Constraint," Papers 2206.04680, arXiv.org.

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