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Optimal dividend problem with a nonlinear regular-singular stochastic control

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  • Chen, Mi
  • Peng, Xiaofan
  • Guo, Junyi

Abstract

In this paper, a problem with a nonlinear regular-singular stochastic control is studied for a big insurance portfolio. We assume that the reinsurance premium is calculated according to the exponential premium principle which makes the stochastic control problem nonlinear. Both non-cheap and cheap reinsurance are investigated. The objective of the insurer is to determine the optimal reinsurance and dividend policy so as to maximize the expected discounted dividends until ruin. Bounded dividend rates and unbounded dividend rates are considered. In both cases, explicit expressions for the value function and the corresponding optimal strategies are obtained. Finally, a numerical example is presented, which shows the impacts of risk aversion of the reinsurance company on the optimal value function and the retention level for reinsurance.

Suggested Citation

  • Chen, Mi & Peng, Xiaofan & Guo, Junyi, 2013. "Optimal dividend problem with a nonlinear regular-singular stochastic control," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 448-456.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:3:p:448-456
    DOI: 10.1016/j.insmatheco.2013.02.010
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    References listed on IDEAS

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    Cited by:

    1. Xiaoqing Liang & Zbigniew Palmowski, 2016. "A note on optimal expected utility of dividend payments with proportional reinsurance," Papers 1605.06849, arXiv.org, revised May 2017.
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    3. Chen, Shumin & Li, Zhongfei & Zeng, Yan, 2014. "Optimal dividend strategies with time-inconsistent preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 150-172.

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    More about this item

    Keywords

    Dividend; Proportional reinsurance; Non-cheap reinsurance; Cheap reinsurance; Exponential premium principle;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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