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Optimal stopping under $\textit{G}$-expectation

Author

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  • Li, Hanwu

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We develop a theory of optimal stopping problems under *G*-expectation framework. We first define a new kind of random times, called *G*-stopping times, which is suitable for this problem. For the discrete time case with finite horizon, the value function is defined backwardly and we show that it is the smallest *G*-supermartingale dominating the payoff process and the optimal stopping time exists. Then we extend this result both to the infinite horizon and to the continuous time case. We also establish the relation between the value function and solution of reflected BSDE driven by *G*-Brownian motion.

Suggested Citation

  • Li, Hanwu, 2019. "Optimal stopping under $\textit{G}$-expectation," Center for Mathematical Economics Working Papers 606, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:606
    as

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    File URL: https://pub.uni-bielefeld.de/download/2933126/2933130
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    References listed on IDEAS

    as
    1. Bayraktar, Erhan & Yao, Song, 2011. "Optimal stopping for non-linear expectations--Part I," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 185-211, February.
    2. 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.
    3. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    4. 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.
    5. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    6. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
    Full references (including those not matched with items on IDEAS)

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