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Time-inconsistent Markovian control problems under model uncertainty with application to the mean-variance portfolio selection

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  • Tomasz R. Bielecki
  • Tao Chen
  • Igor Cialenco

Abstract

In this paper we study a class of time-inconsistent terminal Markovian control problems in discrete time subject to model uncertainty. We combine the concept of the sub-game perfect strategies with the adaptive robust stochastic to tackle the theoretical aspects of the considered stochastic control problem. Consequently, as an important application of the theoretical results, by applying a machine learning algorithm we solve numerically the mean-variance portfolio selection problem under the model uncertainty.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2002.02604
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    References listed on IDEAS

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    1. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2016. "A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective," Papers 1603.09030, arXiv.org, revised Jan 2017.
    2. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    3. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Misspecification," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 6, pages 155-216, World Scientific Publishing Co. Pte. Ltd..
    4. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    5. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2018. "A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 204-221, February.
    6. Tao Chen & Michael Ludkovski, 2019. "A Machine Learning Approach to Adaptive Robust Utility Maximization and Hedging," Papers 1912.00244, arXiv.org, revised May 2020.
    7. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2014. "A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time," Papers 1409.7028, arXiv.org, revised Sep 2017.
    8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    9. Yun Shi & Xiangyu Cui, 2017. "Time Inconsistency and Self-Control Optimization Problems: Progress and Challenges," International Series in Operations Research & Management Science, in: Tsan-Ming Choi & Jianjun Gao & James H. Lambert & Chi-Kong Ng & Jun Wang (ed.), Optimization and Control for Systems in the Big-Data Era, chapter 0, pages 33-42, Springer.
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    Cited by:

    1. Tao Chen & Jiyoun Myung, 2020. "Nonparametric Adaptive Bayesian Stochastic Control Under Model Uncertainty," Papers 2011.04804, arXiv.org, revised Mar 2022.
    2. 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..

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