IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1201.0769.html
   My bibliography  Save this paper

Robust utility maximization in non-dominated models with 2BSDEs

Author

Listed:
  • Anis Matoussi
  • Dylan Possamai
  • Chao Zhou

Abstract

The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is non-dominated. We propose studying this problem in the framework of second-order backward stochastic differential equations (2BSDEs for short) with quadratic growth generators. We show for exponential, power and logarithmic utilities that the value function of the problem can be written as the initial value of a particular 2BSDE and prove existence of an optimal strategy. Finally several examples which shed more light on the problem and its links with the classical utility maximization one are provided. In particular, we show that in some cases, the upper bound of the volatility interval plays a central role, exactly as in the option pricing problem with uncertain volatility models of [2].

Suggested Citation

  • Anis Matoussi & Dylan Possamai & Chao Zhou, 2012. "Robust utility maximization in non-dominated models with 2BSDEs," Papers 1201.0769, arXiv.org, revised Apr 2015.
    • Handle: RePEc:arx:papers:1201.0769
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1201.0769
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    2. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Samuel Drapeau & Peng Luo & Dewen Xiong, 2017. "Characterization of Fully Coupled FBSDE in Terms of Portfolio Optimization," Papers 1703.02694, arXiv.org, revised Sep 2019.
    2. 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.

    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. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    2. 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.
    3. 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.
    4. Hansen, Lars Peter & Sargent, Thomas J., 2022. "Structured ambiguity and model misspecification," Journal of Economic Theory, Elsevier, vol. 199(C).
    5. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    6. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    7. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    8. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    9. Söderlind, Paul, 2009. "The C-CAPM without ex post data," Journal of Macroeconomics, Elsevier, vol. 31(4), pages 721-729, December.
    10. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    11. Kim Weston, 2016. "Stability of utility maximization in nonequivalent markets," Finance and Stochastics, Springer, vol. 20(2), pages 511-541, April.
    12. Wang, Ning & Zhang, Yumo, 2024. "Robust asset-liability management games for n players under multivariate stochastic covariance models," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 67-98.
    13. Elyes Jouini & Pierre-Francois Koehl, "undated". "Pricing of Non-redundant Derivatives in a Complete Market," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-009, New York University, Leonard N. Stern School of Business-.
    14. Chen An & Mahayni Antje B., 2008. "Endowment Assurance Products: Effectiveness of Risk-Minimizing Strategies under Model Risk," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 2(2), pages 1-29, March.
    15. Luo, Yulei & Young, Eric R., 2016. "Induced uncertainty, market price of risk, and the dynamics of consumption and wealth," Journal of Economic Theory, Elsevier, vol. 163(C), pages 1-41.
    16. 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.
    17. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    18. In-Koo Cho & Kenneth Kasa, 2015. "Learning and Model Validation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(1), pages 45-82.
    19. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    20. 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.

    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:1201.0769. 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.