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Adaptive Robust Control Under Model Uncertainty

Author

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  • Tomasz R. Bielecki
  • Tao Chen
  • Igor Cialenco
  • Areski Cousin
  • Monique Jeanblanc

Abstract

In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust control. We demonstrate that the uncertain control problem under consideration can be solved in terms of associated adaptive robust Bellman equation. The success of our approach is to the great extend owed to the recursive methodology for construction of relevant confidence regions. We illustrate our methodology by considering an optimal portfolio allocation problem, and we compare results obtained using the adaptive robust control method with some other existing methods.

Suggested Citation

  • Tomasz R. Bielecki & Tao Chen & Igor Cialenco & Areski Cousin & Monique Jeanblanc, 2017. "Adaptive Robust Control Under Model Uncertainty," Papers 1706.02227, arXiv.org.
    • Handle: RePEc:arx:papers:1706.02227
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    References listed on IDEAS

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    1. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    2. 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..
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    Cited by:

    1. Florian Krach & Josef Teichmann & Hanna Wutte, 2024. "Robust Utility Optimization via a GAN Approach," Papers 2403.15243, arXiv.org.

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