IDEAS home Printed from https://ideas.repec.org/h/wsi/wschap/9789811280306_0005.html
   My bibliography  Save this book chapter

Data-Driven Non-Parametric Robust Control under Dependence Uncertainty

In: Peter Carr Gedenkschrift Research Advances in Mathematical Finance

Author

Listed:
  • Erhan Bayraktar
  • Tao Chen

Abstract

We consider a multi-period stochastic control problem where the multivariate driving stochastic factor of the system has known marginal distributions but uncertain dependence structure. To solve the problem, we propose to implement the non-parametric adaptive robust control framework. We aim to find the optimal control against the worst-case copulae in a sequence of shrinking uncertainty sets which are generated from continuously observing the data. Then, we use a stochastic gradient descent ascent algorithm to numerically handle the corresponding high-dimensional dynamic inf-sup optimization problem. We present the numerical results in the context of utility maximization and show that the controller benefits from knowing more information about the uncertain model.

Suggested Citation

  • Erhan Bayraktar & Tao Chen, 2023. "Data-Driven Non-Parametric Robust Control under Dependence Uncertainty," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 5, pages 141-178, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811280306_0005
    as

    Download full text from publisher

    File URL: https://www.worldscientific.com/doi/pdf/10.1142/9789811280306_0005
    Download Restriction: Ebook Access is available upon purchase.
    File URL: https://www.worldscientific.com/doi/abs/10.1142/9789811280306_0005
    Download Restriction: Ebook Access is available upon purchase.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    2. Erhan Bayraktar & Tao Chen, 2022. "Nonparametric Adaptive Robust Control Under Model Uncertainty," Papers 2202.10391, arXiv.org, revised Mar 2022.
    3. Tomasz R. Bielecki & Tao Chen & Igor Cialenco, 2020. "Time-inconsistent Markovian control problems under model uncertainty with application to the mean-variance portfolio selection," Papers 2002.02604, arXiv.org, revised Sep 2020.
    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. Tao Chen & Jiyoun Myung, 2020. "Nonparametric Adaptive Bayesian Stochastic Control Under Model Uncertainty," Papers 2011.04804, arXiv.org, revised Mar 2022.
    2. Hansen, Lars Peter & Sargent, Thomas J., 2022. "Structured ambiguity and model misspecification," Journal of Economic Theory, Elsevier, vol. 199(C).
    3. Rhys Bidder & Ian Dew-Becker, 2016. "Long-Run Risk Is the Worst-Case Scenario," American Economic Review, American Economic Association, vol. 106(9), pages 2494-2527, September.
    4. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    5. Michael Woodford, 2010. "Robustly Optimal Monetary Policy with Near-Rational Expectations," American Economic Review, American Economic Association, vol. 100(1), pages 274-303, March.
    6. Ralph W. Bailey & Jürgen Eichberger & David Kelsey, 2005. "Ambiguity and Public Good Provision in Large Societies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(5), pages 741-759, December.
    7. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    8. Peter John Robinson & W. J. Wouter Botzen & Fujin Zhou, 2021. "An experimental study of charity hazard: The effect of risky and ambiguous government compensation on flood insurance demand," Journal of Risk and Uncertainty, Springer, vol. 63(3), pages 275-318, December.
    9. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    10. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    11. Richard S. J. Tol & In Chang Hwang & Frédéric Reynès, 2012. "The Effect of Learning on Climate Policy under Fat-tailed Uncertainty," Working Paper Series 5312, Department of Economics, University of Sussex Business School.
    12. Castro, Luciano de & Galvao, Antonio F. & Kim, Jeong Yeol & Montes-Rojas, Gabriel & Olmo, Jose, 2022. "Experiments on portfolio selection: A comparison between quantile preferences and expected utility decision models," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 97(C).
    13. Jürgen Eichberger & Simon Grant & David Kelsey, 2012. "When is ambiguity–attitude constant?," Journal of Risk and Uncertainty, Springer, vol. 45(3), pages 239-263, December.
    14. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    15. Thibaut Mastrolia & Dylan Possamaï, 2018. "Moral Hazard Under Ambiguity," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 452-500, November.
    16. Simona Fabrizi & Steffen Lippert & Addison Pan & Matthew Ryan, 2022. "A theory of unanimous jury voting with an ambiguous likelihood," Theory and Decision, Springer, vol. 93(3), pages 399-425, October.
    17. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2019. "Dynamic risk measures for processes via backward stochastic differential equations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 43-50.
    18. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    19. ,, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    20. Kiyohiko G. Nishimura & Hiroyuki Ozaki, 2001. "Search under the Knightian Uncertainty," CIRJE F-Series CIRJE-F-112, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item

    Keywords

    Mathematical Finance; Quantitative Finance; Option Pricing; Derivatives; No Arbitrage; Asset Price Bubbles; Asset Pricing; Equilibrium; Volatility; Diffusion Processes; Jump Processes; Stochastic Integration; Trading Strategies; Portfolio Theory; Optimization; Securities; Bonds; Commodities; Futures;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    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:wsi:wschap:9789811280306_0005. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscientific.com/page/worldscibooks .

    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.