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Reflected backward stochastic differential equation driven by $\textit{G}$-Brownian motion with an upper obstacle

Author

Listed:
  • Li, Hanwu

    (Center for Mathematical Economics, Bielefeld University)

  • Peng, Shige

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper, we study the reflected backward stochastic differential equation driven by $\textit{G}$- Brownian motion (reflected $\textit{G}$-BSDE for short) with an upper obstacle. The existence is proved by approximation via penalization. By using a variant comparison theorem, we show that the solution we constructed is the largest one.

Suggested Citation

  • Li, Hanwu & Peng, Shige, 2025. "Reflected backward stochastic differential equation driven by $\textit{G}$-Brownian motion with an upper obstacle," Center for Mathematical Economics Working Papers 715, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:715
    as

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    File URL: https://pub.uni-bielefeld.de/download/3004917/3004918
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    References listed on IDEAS

    as
    1. Lepeltier, J.-P. & Xu, M., 2005. "Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 58-66, November.
    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. Hamadène, S. & Lepeltier, J. -P., 2000. "Reflected BSDEs and mixed game problem," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 177-188, February.
    4. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
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