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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
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    References listed on IDEAS

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    1. Erhan Bayraktar & Tao Chen, 2022. "Nonparametric Adaptive Robust Control Under Model Uncertainty," Papers 2202.10391, arXiv.org, revised Mar 2022.
    2. 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.
    3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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    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

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