IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2508.12047.html
   My bibliography  Save this paper

Equilibrium Mean-Variance Dividend Rate Strategies

Author

Listed:
  • Jingyi Cao
  • Dongchen Li
  • Virginia R. Young
  • Bin Zou

Abstract

This paper studies an optimal dividend problem for a company that aims to maximize the mean-variance (MV) objective of the accumulated discounted dividend payments up to its ruin time. The MV objective involves an integral form over a random horizon that depends endogenously on the company's dividend strategy, and these features lead to a novel time-inconsistent control problem. To address the time inconsistency, we seek a time-consistent equilibrium dividend rate strategy. We first develop and prove a new verification lemma that characterizes the value function and equilibrium strategy by an extended Hamilton-Jacobi-Bellman system. Next, we apply the verification lemma to obtain the equilibrium strategy and show that it is a barrier strategy for small levels of risk aversion.

Suggested Citation

  • Jingyi Cao & Dongchen Li & Virginia R. Young & Bin Zou, 2025. "Equilibrium Mean-Variance Dividend Rate Strategies," Papers 2508.12047, arXiv.org.
    • Handle: RePEc:arx:papers:2508.12047
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2508.12047
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Chonghu Guan & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org, revised Jul 2024.
    3. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    4. 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.
    5. 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.
    6. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2018. "Optimal Dividend Distribution Under Drawdown and Ratcheting Constraints on Dividend Rates," Papers 1806.07499, arXiv.org, revised Mar 2019.
    7. 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.
    8. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    9. Michael I. Taksar, 2000. "Optimal risk and dividend distribution control models for an insurance company," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(1), pages 1-42, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chonghu Guan & Jiacheng Fan & Zuo Quan Xu, 2023. "Optimal dividend payout with path-dependent drawdown constraint," Papers 2312.01668, arXiv.org.
    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. 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.
    4. Mingxin Guo & Zuo Quan Xu, 2024. "Stochastic optimal self-path-dependent control: A new type of variational inequality and its viscosity solution," Papers 2412.11383, arXiv.org.
    5. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2020. "Optimal ratcheting of dividends in a Brownian risk model," Papers 2012.10632, arXiv.org.
    6. 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.
    7. Peter Grandits, 2015. "An optimal consumption problem in finite time with a constraint on the ruin probability," Finance and Stochastics, Springer, vol. 19(4), pages 791-847, October.
    8. Ernst, Philip A. & Imerman, Michael B. & Shepp, Larry & Zhou, Quan, 2022. "Fiscal stimulus as an optimal control problem," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1091-1108.
    9. Hansjörg Albrecher & Pablo Azcue & Nora Muler, 2023. "Optimal dividends under a drawdown constraint and a curious square-root rule," Finance and Stochastics, Springer, vol. 27(2), pages 341-400, April.
    10. Chonghu Guan & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org, revised Jul 2024.
    11. 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.
    12. 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.
    13. Feng, Yang & Siu, Tak Kuen & Zhu, Jinxia, 2024. "Optimal payout strategies when Bruno de Finetti meets model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 148-164.
    14. Kristoffer Lindensjö & Filip Lindskog, 2020. "Optimal dividends and capital injection under dividend restrictions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 461-487, December.
    15. Guan, Huiqi & Liang, Zongxia, 2014. "Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 109-122.
    16. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2022. "Optimal dividends under a drawdown constraint and a curious square-root rule," Papers 2206.12220, arXiv.org.
    17. Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1-2), pages 211-218, January.
    18. Liang, Zhibin & Young, Virginia R., 2012. "Dividends and reinsurance under a penalty for ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 437-445.
    19. Hubalek, Friedrich & Schachermayer, Walter, 2004. "Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 193-225, April.
    20. Julia Eisenberg & Paul Kruhner, 2018. "Suboptimal Control of Dividends under Exponential Utility," Papers 1809.01983, arXiv.org, revised Jan 2019.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2508.12047. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.