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An Optimal Control Problem in a Risk Model with Stochastic Premiums and Periodic Dividend Payments

Author

Listed:
  • Xixi Yang

    (School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P. R. China)

  • Jiyang Tan

    (School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P. R. China)

  • Hanjun Zhang

    (School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P. R. China)

  • Ziqiang Li

    (School of Information Engineering, Xiangtan University, Xiangtan 411105, P. R. China)

Abstract

In this paper, a discrete-time risk model is considered. We assume that the premium received in each time interval is a positive real-valued random variable, and the sequence of premiums is a Markov chain. In any time interval the probability of a claim occurrence is related to the premium received in the corresponding period. We discuss control strategies for dividends paid periodically to the shareholders under two cases: absence and presence of ceiling restriction for dividend rates. We provide algorithms and some properties for the optimal control strategies by transforming the value function.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:apjorx:v:34:y:2017:i:03:n:s0217595917400139
    DOI: 10.1142/S0217595917400139
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    References listed on IDEAS

    as
    1. 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.
    2. Avanzi, Benjamin & Tu, Vincent & Wong, Bernard, 2014. "On optimal periodic dividend strategies in the dual model with diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 210-224.
    3. Zhu, Jinxia & Chen, Feng, 2015. "Dividend optimization under reserve constraints for the Cramér–Lundberg model compounded by force of interest," Economic Modelling, Elsevier, vol. 46(C), pages 142-156.
    4. Albrecher, Hansjörg & Cheung, Eric C.K. & Thonhauser, Stefan, 2011. "Randomized Observation Periods for the Compound Poisson Risk Model: Dividends," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 645-672, November.
    5. Zhuo Jin & G. Yin, 2013. "Numerical Methods for Optimal Dividend Payment and Investment Strategies of Markov-Modulated Jump Diffusion Models with Regular and Singular Controls," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 246-271, October.
    6. Choi, Michael C.H. & Cheung, Eric C.K., 2014. "On the expected discounted dividends in the Cramér–Lundberg risk model with more frequent ruin monitoring than dividend decisions," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 121-132.
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