IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2306.01503.html
   My bibliography  Save this paper

Strategies with minimal norm are optimal for expected utility maximization under high model ambiguity

Author

Listed:
  • Laurence Carassus
  • Johannes Wiesel

Abstract

We investigate an expected utility maximization problem under model uncertainty in a one-period financial market. We capture model uncertainty by replacing the baseline model $\mathbb{P}$ with an adverse choice from a Wasserstein ball of radius $k$ around $\mathbb{P}$ in the space of probability measures and consider the corresponding Wasserstein distributionally robust optimization problem. We show that optimal solutions converge to a strategy with minimal norm when uncertainty is increasingly large, i.e. when the radius $k$ tends to infinity.

Suggested Citation

  • Laurence Carassus & Johannes Wiesel, 2023. "Strategies with minimal norm are optimal for expected utility maximization under high model ambiguity," Papers 2306.01503, arXiv.org, revised Jan 2024.
  • Handle: RePEc:arx:papers:2306.01503
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2306.01503
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hansen, Lars Peter & Sargent, Thomas J., 2011. "Robustness and ambiguity in continuous time," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1195-1223, May.
    2. Erhan Bayraktar & Zhou Zhou, 2017. "On Arbitrage And Duality Under Model Uncertainty And Portfolio Constraints," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 988-1012, October.
    3. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    4. Romain Blanchard & Laurence Carassus, 2018. "Multiple-Priors Optimal Investment In Discrete Time For Unbounded Utility Function," Working Papers hal-01883787, HAL.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    7. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    8. Pflug, Georg Ch. & Pichler, Alois & Wozabal, David, 2012. "The 1/N investment strategy is optimal under high model ambiguity," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 410-417.
    9. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
    10. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    11. Kerkhof, Jeroen & Melenberg, Bertrand & Schumacher, Hans, 2010. "Model risk and capital reserves," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 267-279, January.
    12. Jorn Sass & Dorothee Westphal, 2020. "Robust Utility Maximization in a Multivariate Financial Market with Stochastic Drift," Papers 2009.14559, arXiv.org, revised May 2021.
    13. Jan Obloj & Johannes Wiesel, 2021. "Distributionally robust portfolio maximisation and marginal utility pricing in one period financial markets," Papers 2105.00935, arXiv.org, revised Nov 2021.
    14. Jan Obłój & Johannes Wiesel, 2021. "Distributionally robust portfolio maximization and marginal utility pricing in one period financial markets," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1454-1493, October.
    15. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    16. Jörn Sass & Dorothee Westphal, 2021. "Robust Utility Maximization In A Multivariate Financial Market With Stochastic Drift," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 1-28, June.
    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. Ariel Neufeld & Matthew Ng Cheng En & Ying Zhang, 2024. "Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems," Papers 2403.09532, arXiv.org.
    2. Jan Obłój & Johannes Wiesel, 2021. "Distributionally robust portfolio maximization and marginal utility pricing in one period financial markets," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1454-1493, October.
    3. Ariel Neufeld & Julian Sester, 2024. "Non-concave distributionally robust stochastic control in a discrete time finite horizon setting," Papers 2404.05230, arXiv.org.
    4. Daniel Bartl & Ariel Neufeld & Kyunghyun Park, 2023. "Sensitivity of robust optimization problems under drift and volatility uncertainty," Papers 2311.11248, arXiv.org.
    5. Jorn Sass & Dorothee Westphal, 2019. "Robust Utility Maximizing Strategies under Model Uncertainty and their Convergence," Papers 1909.01830, arXiv.org, revised Nov 2021.
    6. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    7. Michail Anthropelos & Paul Schneider, 2021. "Optimal Investment and Equilibrium Pricing under Ambiguity," Swiss Finance Institute Research Paper Series 21-78, Swiss Finance Institute.
    8. Laurence Carassus & Massinissa Ferhoune, 2024. "Nonconcave Robust Utility Maximization under Projective Determinacy," Papers 2403.11824, arXiv.org.
    9. Len Patrick Dominic M. Garces & Yang Shen, 2024. "Robust optimal investment and consumption strategies with portfolio constraints and stochastic environment," Papers 2407.02831, arXiv.org.
    10. Yanwei Jia, 2024. "Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penalty," Papers 2404.12598, arXiv.org.
    11. Jan Obloj & Johannes Wiesel, 2021. "Distributionally robust portfolio maximisation and marginal utility pricing in one period financial markets," Papers 2105.00935, arXiv.org, revised Nov 2021.
    12. Jorn Sass & Dorothee Westphal, 2020. "Robust Utility Maximization in a Multivariate Financial Market with Stochastic Drift," Papers 2009.14559, arXiv.org, revised May 2021.
    13. Miklós Rásonyi & Andrea Meireles‐Rodrigues, 2021. "On utility maximization under model uncertainty in discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 149-175, January.
    14. Blanchard, Romain & Carassus, Laurence, 2020. "No-arbitrage with multiple-priors in discrete time," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6657-6688.
    15. Qian Lin & Frank Riedel, 2021. "Optimal consumption and portfolio choice with ambiguous interest rates and volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1189-1202, April.
    16. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    17. Yacine Aït-Sahalia & Felix Matthys & Emilio Osambela & Ronnie Sircar, 2021. "When Uncertainty and Volatility Are Disconnected: Implications for Asset Pricing and Portfolio Performance," NBER Working Papers 29195, National Bureau of Economic Research, Inc.
    18. Daniel Bartl, 2016. "Exponential utility maximization under model uncertainty for unbounded endowments," Papers 1610.00999, arXiv.org, revised Feb 2019.
    19. Erhan Bayraktar & Tao Chen, 2022. "Nonparametric Adaptive Robust Control Under Model Uncertainty," Papers 2202.10391, arXiv.org, revised Mar 2022.
    20. Laurence Carassus & Massinissa Ferhoune, 2023. "Discrete time optimal investment under model uncertainty," Papers 2307.11919, arXiv.org, revised Feb 2024.

    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:2306.01503. 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.