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Optimal dividend strategies in a delayed claim risk model with dividends discounted by stochastic interest rates

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Listed:
  • Jiyang Tan
  • Chun Li
  • Ziqiang Li
  • Xiangqun Yang
  • Bicheng Zhang

Abstract

We consider a discrete-time risk model with delayed claims and a dividend payment strategy. It is assumed that every main claim will induce a by-claim which may be delayed for one time period with a certain probability. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. Dividends are paid to the shareholders according to an admissible strategy. The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin minus the expected discounted penalty value at ruin. We obtain some properties of the optimal dividend-payment strategy, and offer high efficiency algorithms for obtaining the optimal strategy, the optimal value function and the expectation of time of ruin under the optimal strategy. Our method is mainly to transform the value function. Numerical examples are presented to illustrate the transformation method and the impact of the penalty for ruin on the optimal strategy, the corresponding expected present value of dividends and the expectation of time of ruin. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Jiyang Tan & Chun Li & Ziqiang Li & Xiangqun Yang & Bicheng Zhang, 2015. "Optimal dividend strategies in a delayed claim risk model with dividends discounted by stochastic interest rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 61-83, August.
    • Handle: RePEc:spr:mathme:v:82:y:2015:i:1:p:61-83
    DOI: 10.1007/s00186-015-0504-2
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    References listed on IDEAS

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    Cited by:

    1. Elena Bandini & Tiziano De Angelis & Giorgio Ferrari & Fausto Gozzi, 2022. "Optimal dividend payout under stochastic discounting," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 627-677, April.
    2. Yangmin Zhong & Huaping Huang, 2023. "Cash Flow Optimization on Insurance: An Application of Fixed-Point Theory," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
    3. Xixi Yang & Jiyang Tan & Hanjun Zhang & Ziqiang Li, 2017. "An Optimal Control Problem in a Risk Model with Stochastic Premiums and Periodic Dividend Payments," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(03), pages 1-18, June.

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    More about this item

    Keywords

    Delayed claim; Optimal dividend strategy; Penalty for ruin; Time of ruin; Transformation; G22; G35;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy

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