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Singular dividend optimization for a linear diffusion model with time-inconsistent preferences

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  • Zhu, Jinxia
  • Siu, Tak Kuen
  • Yang, Hailiang

Abstract

With the advancement of behavioral economics, the use of exponential discounting for decision making in neoclassical economics has been questioned since it cannot provide a realistic way to explain certain decision-making behavior.The purpose of this paper is to investigate strategic decision making on dividend distribution policies of insurance companies when the management adopts a more realistic way for discounting, namely stochastic quasi-hyperbolic discounting. The use of this more realistic way for discounting is motivated by some recent developments in behavioral economics. A game theoretic approach is adopted to establish economic equilibrium results, namely subgame perfect Markov equilibrium strategies. It is shown that (1) under certain mild technical conditions, the barrier strategy with an optimal barrier, which is widely used in the traditional approach to optimal dividend problems, is a perfect Markov equilibrium strategy, (2) the optimal barrier is lower than the barrier of an optimal strategy obtained from the respective time-consistent optimal dividend problem, and (3) the solution based on the barrier strategy does not exist in some situations.

Suggested Citation

  • Zhu, Jinxia & Siu, Tak Kuen & Yang, Hailiang, 2020. "Singular dividend optimization for a linear diffusion model with time-inconsistent preferences," European Journal of Operational Research, Elsevier, vol. 285(1), pages 66-80.
    • Handle: RePEc:eee:ejores:v:285:y:2020:i:1:p:66-80
    DOI: 10.1016/j.ejor.2019.04.027
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    References listed on IDEAS

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    Cited by:

    1. Brinker, Leonie Violetta & Eisenberg, Julia, 2021. "Dividend optimisation: A behaviouristic approach," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 202-224.
    2. Zhuo Jin & Zuo Quan Xu & Bin Zou, 2020. "A Perturbation Approach to Optimal Investment, Liability Ratio, and Dividend Strategies," Papers 2012.06703, arXiv.org, revised May 2021.
    3. Julia Eisenberg & Stefan Kremsner & Alexander Steinicke, 2021. "Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate," Papers 2108.00234, arXiv.org.
    4. Gaïgi, M’hamed & Ly Vath, Vathana & Scotti, Simone, 2022. "Optimal harvesting under marine reserves and uncertain environment," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1181-1194.
    5. Wenyuan Wang & Xiang Yu & Xiaowen Zhou, 2021. "On optimality of barrier dividend control under endogenous regime switching with application to Chapter 11 bankruptcy," Papers 2108.01800, arXiv.org, revised Nov 2023.
    6. Julia Eisenberg & Stefan Kremsner & Alexander Steinicke, 2021. "Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate," Mathematics, MDPI, vol. 9(18), pages 1-20, September.
    7. Zhou, Zhou & Jin, Zhuo, 2020. "Optimal equilibrium barrier strategies for time-inconsistent dividend problems in discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 100-108.

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