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Stochastic Optimal Control Problem with Obstacle Constraints in Sublinear Expectation Framework

Author

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  • Li, Hanwu

    (Center for Mathematical Economics, Bielefeld University)

  • Wang, Falei

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper we consider a stochastic optimal control problem, in which the cost function is defined through a reflected backward stochastic differential equation in sublinear expectation framework. Besides, we study the regularity of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the unique viscosity solution of the related Hamilton-Jacobi-Bellman-Isaac equation.

Suggested Citation

  • Li, Hanwu & Wang, Falei, 2025. "Stochastic Optimal Control Problem with Obstacle Constraints in Sublinear Expectation Framework," Center for Mathematical Economics Working Papers 719, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:719
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    File URL: https://pub.uni-bielefeld.de/download/3005045/3005046
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    References listed on IDEAS

    as
    1. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Backward stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 759-784.
    2. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.
    3. Hu, Mingshang & Ji, Shaolin, 2017. "Dynamic programming principle for stochastic recursive optimal control problem driven by a G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 107-134.
    4. Li, Hanwu & Peng, Shige & Soumana Hima, Abdoulaye, 2018. "Reflected Solutions of BSDEs Driven by $\textit{G}$-Brownian Motion," Center for Mathematical Economics Working Papers 590, Center for Mathematical Economics, Bielefeld University.
    5. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1170-1195.
    6. Ariel Neufeld & Marcel Nutz, 2018. "Robust Utility Maximization With Lã‰Vy Processes," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 82-105, January.
    Full references (including those not matched with items on IDEAS)

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