IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2012.10632.html
   My bibliography  Save this paper

Optimal ratcheting of dividends in a Brownian risk model

Author

Listed:
  • Hansjoerg Albrecher
  • Pablo Azcue
  • Nora Muler

Abstract

We study the problem of optimal dividend payout from a surplus process governed by Brownian motion with drift under the additional constraint of ratcheting, i.e. the dividend rate can never decrease. We solve the resulting two-dimensional optimal control problem, identifying the value function to be the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. For finitely many admissible dividend rates we prove that threshold strategies are optimal, and for any finite continuum of admissible dividend rates we establish the $\varepsilon$-optimality of curve strategies. This work is a counterpart of Albrecher et al. (2020), where the ratcheting problem was studied for a compound Poisson surplus process with drift. In the present Brownian setup, calculus of variation techniques allow to obtain a much more explicit analysis and description of the optimal dividend strategies. We also give some numerical illustrations of the optimality results.

Suggested Citation

  • Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2020. "Optimal ratcheting of dividends in a Brownian risk model," Papers 2012.10632, arXiv.org.
    • Handle: RePEc:arx:papers:2012.10632
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2012.10632
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2020. "Optimal Consumption under a Habit-Formation Constraint: the Deterministic Case," Papers 2012.02277, arXiv.org, revised Oct 2022.
    2. Zhou Yang & Hyeng Keun Koo, 2018. "Optimal Consumption and Portfolio Selection with Early Retirement Option," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1378-1404, November.
    3. Romuald Elie & Nizar Touzi, 2008. "Optimal lifetime consumption and investment under a drawdown constraint," Finance and Stochastics, Springer, vol. 12(3), pages 299-330, July.
    4. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    5. Philip H. Dybvig, 1995. "Dusenberry's Ratcheting of Consumption: Optimal Dynamic Consumption and Investment Given Intolerance for any Decline in Standard of Living," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(2), pages 287-313.
    6. Hansjoerg Albrecher & Nicole Bäuerle & Martin Bladt, 2018. "Dividends: From Refracting to Ratcheting," Swiss Finance Institute Research Paper Series 18-32, Swiss Finance Institute.
    7. Asaf Cohen & Virginia R. Young, 2019. "Rate of Convergence of the Probability of Ruin in the Cram\'er-Lundberg Model to its Diffusion Approximation," Papers 1902.00706, arXiv.org, revised Jun 2020.
    8. 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.
    9. Benjamin Avanzi & Vincent Tu & Bernard Wong, 2016. "A Note on Realistic Dividends in Actuarial Surplus Models," Risks, MDPI, vol. 4(4), pages 1-9, October.
    10. Jeon, Junkee & Koo, Hyeng Keun & Shin, Yong Hyun, 2018. "Portfolio selection with consumption ratcheting," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 153-182.
    11. 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.
    12. Cohen, Asaf & Young, Virginia R., 2020. "Rate of convergence of the probability of ruin in the Cramér–Lundberg model to its diffusion approximation," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 333-340.
    13. Albrecher, Hansjörg & Bäuerle, Nicole & Bladt, Martin, 2018. "Dividends: From refracting to ratcheting," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 47-58.
    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 & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org.
    2. 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.
    3. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2022. "Optimal dividends under a drawdown constraint and a curious square-root rule," Papers 2206.12220, arXiv.org.
    4. Chonghu Guan & Jiacheng Fan & Zuo Quan Xu, 2023. "Optimal dividend payout with path-dependent drawdown constraint," Papers 2312.01668, arXiv.org.
    5. 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.
    6. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2019. "Optimal ratcheting of dividends in insurance," Papers 1910.06910, arXiv.org, revised Jun 2021.
    7. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2021. "Optimal Investment and Consumption under a Habit-Formation Constraint," Papers 2102.03414, arXiv.org, revised Nov 2021.
    8. Junkee Jeon & Kyunghyun Park, 2021. "Portfolio selection with drawdown constraint on consumption: a generalization model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 243-289, April.
    9. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2020. "Optimal Consumption under a Habit-Formation Constraint: the Deterministic Case," Papers 2012.02277, arXiv.org, revised Oct 2022.
    10. Choi, Kyoung Jin & Jeon, Junkee & Koo, Hyeng Keun, 2022. "Intertemporal preference with loss aversion: Consumption and risk-attitude," Journal of Economic Theory, Elsevier, vol. 200(C).
    11. Albrecher, Hansjörg & Bäuerle, Nicole & Bladt, Martin, 2018. "Dividends: From refracting to ratcheting," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 47-58.
    12. Benjamin Avanzi & Debbie Kusch Falden & Mogens Steffensen, 2022. "Stable Dividends under Linear-Quadratic Optimization," Papers 2210.03494, arXiv.org.
    13. Julia Eisenberg & Paul Kruhner, 2018. "Suboptimal Control of Dividends under Exponential Utility," Papers 1809.01983, arXiv.org, revised Jan 2019.
    14. 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.
    15. Li, Xun & Yu, Xiang & Zhang, Qinyi, 2023. "Optimal consumption and life insurance under shortfall aversion and a drawdown constraint," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 25-45.
    16. Benjamin Avanzi & Hayden Lau & Bernard Wong, 2020. "On the optimality of joint periodic and extraordinary dividend strategies," Papers 2006.00717, arXiv.org, revised Dec 2020.
    17. Avanzi, Benjamin & Lau, Hayden & Wong, Bernard, 2021. "On the optimality of joint periodic and extraordinary dividend strategies," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1189-1210.
    18. 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.
    19. Ying Shen & Chuancun Yin & Kam Chuen Yuen, 2011. "Alternative approach to the optimality of the threshold strategy for spectrally negative Levy processes," Papers 1101.0446, arXiv.org, revised Feb 2014.
    20. Szölgyenyi Michaela, 2015. "Dividend maximization in a hidden Markov switching model," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 143-158, December.

    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:2012.10632. 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.