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Data-Driven Nonparametric Robust Control under Dependence Uncertainty

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  • 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 nonparametric 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.

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  • Erhan Bayraktar & Tao Chen, 2022. "Data-Driven Nonparametric Robust Control under Dependence Uncertainty," Papers 2209.04976, arXiv.org.
    • Handle: RePEc:arx:papers:2209.04976
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    References listed on IDEAS

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