IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2503.08272.html
   My bibliography  Save this paper

Dynamically optimal portfolios for monotone mean--variance preferences

Author

Listed:
  • Alev{s} v{C}ern'y
  • Johannes Ruf
  • Martin Schweizer

Abstract

Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal dynamic portfolio choice for the MMV utility in asset price models with independent returns. The task is performed under minimal assumptions, weaker than the existence of an equivalent martingale measure and with no restrictions on the moments of asset returns. We interpret the maximal MMV utility in terms of the monotone Sharpe ratio (MSR) and show that the global squared MSR arises as the nominal yield from continuously compounding at the rate equal to the maximal local squared MSR. The paper gives simple necessary and sufficient conditions for mean-variance (MV) efficient portfolios to be MMV efficient. Several illustrative examples contrasting the MV and MMV criteria are provided.

Suggested Citation

  • Alev{s} v{C}ern'y & Johannes Ruf & Martin Schweizer, 2025. "Dynamically optimal portfolios for monotone mean--variance preferences," Papers 2503.08272, arXiv.org.
    • Handle: RePEc:arx:papers:2503.08272
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2503.08272
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Aleš Černý, 2003. "Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets," Review of Finance, European Finance Association, vol. 7(2), pages 191-233.
    2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean‐Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521, July.
    3. Fabio Bellini & Marco Frittelli, 2002. "On the Existence of Minimax Martingale Measures," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 1-21, January.
    4. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    5. Aleš Černý, 2020. "Semimartingale theory of monotone mean–variance portfolio allocation," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1168-1178, July.
    6. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    7. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
    8. Alev{s} v{C}ern'y & Johannes Ruf, 2020. "Simplified stochastic calculus via semimartingale representations," Papers 2006.11914, arXiv.org, revised Jan 2022.
    9. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    10. Filipovic, Damir & Kupper, Michael, 2007. "Monotone and cash-invariant convex functions and hulls," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 1-16, July.
    11. Jan Kallsen, 2000. "Optimal portfolios for exponential Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 357-374, August.
    12. Esche, Felix & Schweizer, Martin, 2005. "Minimal entropy preserves the Lévy property: how and why," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 299-327, February.
    13. Jakub Trybuła & Dariusz Zawisza, 2019. "Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 966-987, August.
    14. Christian Bender & Christina Niethammer, 2008. "On q-optimal martingale measures in exponential Lévy models," Finance and Stochastics, Springer, vol. 12(3), pages 381-410, July.
    15. Constantinos Kardaras, 2009. "No‐Free‐Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 161-187, April.
    16. Black, Fischer & Perold, AndreF., 1992. "Theory of constant proportion portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 403-426.
    17. Jan Kallsen, 1999. "A utility maximization approach to hedging in incomplete markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 321-338, October.
    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. Constantinos Kardaras, 2009. "No‐Free‐Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 161-187, April.
    2. Černý, Aleš & Ruf, Johannes, 2021. "Simplified stochastic calculus with applications in Economics and Finance," European Journal of Operational Research, Elsevier, vol. 293(2), pages 547-560.
    3. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    4. Černý, Aleš & Ruf, Johannes, 2023. "Simplified calculus for semimartingales: Multiplicative compensators and changes of measure," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 572-602.
    5. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean‐Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521, July.
    6. Friedrich Hubalek & Carlo Sgarra, 2006. "Esscher transforms and the minimal entropy martingale measure for exponential Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 125-145.
    7. Aleš Černý, 2020. "Semimartingale theory of monotone mean–variance portfolio allocation," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1168-1178, July.
    8. Černý, Aleš & Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2012. "On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 386-395.
    9. Antonis Papapantoleon, 2008. "An introduction to L\'{e}vy processes with applications in finance," Papers 0804.0482, arXiv.org, revised Nov 2008.
    10. Klöppel Susanne & Schweizer Martin, 2007. "Dynamic utility-based good deal bounds," Statistics & Risk Modeling, De Gruyter, vol. 25(4), pages 285-309, October.
    11. Yang Shen & Bin Zou, 2022. "Cone-constrained Monotone Mean-Variance Portfolio Selection Under Diffusion Models," Papers 2205.15905, arXiv.org.
    12. Nendel, Max & Riedel, Frank & Schmeck, Maren Diane, 2021. "A decomposition of general premium principles into risk and deviation," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 193-209.
    13. Bohan Li & Junyi Guo & Xiaoqing Liang, 2025. "Optimal Monotone Mean-Variance Problem in a Catastrophe Insurance Model," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-37, March.
    14. He, Ying & Dyer, James S. & Butler, John C. & Jia, Jianmin, 2019. "An additive model of decision making under risk and ambiguity," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 78-92.
    15. Gu, Lingqi & Lin, Yiqing & Yang, Junjian, 2016. "On the dual problem of utility maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1019-1035.
    16. Lioudmila Vostrikova & Yuchao Dong, 2018. "Utility maximization for L{\'e}vy switching models," Papers 1807.08982, arXiv.org.
    17. Kozhan, Roman & Salmon, Mark, 2009. "Uncertainty aversion in a heterogeneous agent model of foreign exchange rate formation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1106-1122, May.
    18. Xiaomin Shi & Zuo Quan Xu, 2024. "Constrained monotone mean--variance investment-reinsurance under the Cram\'er--Lundberg model with random coefficients," Papers 2405.17841, arXiv.org, revised May 2024.
    19. Küchler Uwe & Tappe Stefan, 2009. "Option pricing in bilateral Gamma stock models," Statistics & Risk Modeling, De Gruyter, vol. 27(4), pages 281-307, December.
    20. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.

    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:2503.08272. 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.