IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2511.08433.html

Equilibrium Strategies for Singular Dividend Control Problems under the Mean-Variance Criterion

Author

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

Abstract

We revisit the optimal dividend problem of de Finetti by adding a variance term to the usual criterion of maximizing the expected discounted dividends paid until ruin, in a singular control framework. Investors do not like variability in their dividend distribution, and the mean-variance (MV) criterion balances the desire for large expected dividend payments with small variability in those payments. The resulting MV singular dividend control problem is time-inconsistent, and we follow a game-theoretic approach to find a time-consistent equilibrium strategy. Our main contribution is a new verification theorem for the novel dividend problem, in which the MV criterion is applied to an integral of the control until ruin, a random time that is endogenous to the problem. We demonstrate the use of the verification theorem in two cases for which we obtain the equilibrium dividend strategy (semi-)explicitly, and we provide a numerical example to illustrate our results.

Suggested Citation

  • Jingyi Cao & Dongchen Li & Virginia R. Young & Bin Zou, 2025. "Equilibrium Strategies for Singular Dividend Control Problems under the Mean-Variance Criterion," Papers 2511.08433, arXiv.org.
    • Handle: RePEc:arx:papers:2511.08433
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2511.08433
    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. Erhan Bayraktar & Jingjie Zhang & Zhou Zhou, 2018. "Time Consistent Stopping For The Mean-Standard Deviation Problem --- The Discrete Time Case," Papers 1802.08358, arXiv.org, revised Apr 2019.
    3. Chonghu Guan & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org, revised Jul 2024.
    4. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    5. 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.
    6. Amine Ismail & Huyên Pham, 2019. "Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix," Post-Print hal-03947497, HAL.
    7. Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    8. Erhan Bayraktar & Jingjie Zhang & Zhou Zhou, 2021. "Equilibrium concepts for time‐inconsistent stopping problems in continuous time," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 508-530, January.
    9. 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.
    10. Jingyi Cao & Dongchen Li & Virginia R. Young & Bin Zou, 2025. "Equilibrium Mean-Variance Dividend Rate Strategies," Papers 2508.12047, arXiv.org.
    11. Amine Ismail & Huyên Pham, 2019. "Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 174-207, January.
    12. 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.
    13. Yu-Jui Huang & Zhou Zhou, 2021. "Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 428-451, May.
    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. Jingyi Cao & Dongchen Li & Virginia R. Young & Bin Zou, 2025. "Equilibrium Mean-Variance Dividend Rate Strategies," Papers 2508.12047, arXiv.org.
    2. Chonghu Guan & Jiacheng Fan & Zuo Quan Xu, 2023. "Optimal dividend payout with path-dependent drawdown constraint," Papers 2312.01668, arXiv.org, revised Jan 2026.
    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. Oumar Mbodji & Traian A. Pirvu, 2025. "Portfolio time consistency and utility weighted discount rates," Mathematics and Financial Economics, Springer, volume 19, number 2, December.
    5. 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.
    6. 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.
    7. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2020. "Optimal ratcheting of dividends in a Brownian risk model," Papers 2012.10632, arXiv.org.
    8. 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.
    9. Pulak Swain & Akshay Kumar Ojha, 2025. "Feasibility conditions of robust portfolio solutions with single and combined uncertainties," OPSEARCH, Springer;Operational Research Society of India, vol. 62(3), pages 1262-1287, September.
    10. Yu-Jui Huang & Zhenhua Wang, 2020. "Optimal Equilibria for Multi-dimensional Time-inconsistent Stopping Problems," Papers 2006.00754, arXiv.org, revised Jan 2021.
    11. Pengyu Wei & Wei Wei, 2024. "Irreversible investment under weighted discounting: effects of decreasing impatience," Papers 2409.01478, arXiv.org.
    12. Kristoffer Lindensjo & Filip Lindskog, 2019. "Optimal dividends and capital injection under dividend restrictions," Papers 1902.06294, arXiv.org.
    13. 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.
    14. Feng, Runhuan & Jing, Xiaochen & Ng, Kenneth Tsz Hin, 2025. "Optimal investment-withdrawal strategy for variable annuities under a performance fee structure," Journal of Economic Dynamics and Control, Elsevier, vol. 170(C).
    15. 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.
    16. Chonghu Guan & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org, revised Jul 2024.
    17. Živkov, Dejan & Balaban, Suzana & Simić, Milica, 2024. "Hedging gas in a multi-frequency semiparametric CVaR portfolio," Research in International Business and Finance, Elsevier, vol. 67(PA).
    18. Soren Christensen & Kristoffer Lindensjo, 2019. "Moment constrained optimal dividends: precommitment \& consistent planning," Papers 1909.10749, arXiv.org.
    19. Soren Christensen & Kristoffer Lindensjo, 2019. "Time-inconsistent stopping, myopic adjustment & equilibrium stability: with a mean-variance application," Papers 1909.11921, arXiv.org, revised Jan 2020.
    20. Jian-hao Kang & Nan-jing Huang & Ben-Zhang Yang & Zhihao Hu, 2025. "Robust Equilibrium Strategy for Mean–Variance–Skewness Portfolio Selection Problem with Long Memory," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-47, August.

    More about this item

    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:2511.08433. 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.