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Multi-dimensional Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Diagonal Generators

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  • Hanwu Li

    (Shandong University
    Shandong University)

  • Guomin Liu

    (Nankai University)

Abstract

We consider the well-posedness problem of multi-dimensional reflected backward stochastic differential equations driven by G-Brownian motion (G-BSDEs) with diagonal generators. Two methods, including the penalization method and the Picard iteration argument, are provided to prove the existence and uniqueness of the solutions. We also study its connection with the obstacle problem of a system of fully nonlinear PDEs.

Suggested Citation

  • Hanwu Li & Guomin Liu, 2024. "Multi-dimensional Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Diagonal Generators," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2615-2645, September.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:3:d:10.1007_s10959-024-01334-4
    DOI: 10.1007/s10959-024-01334-4
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    References listed on IDEAS

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    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. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2017. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Post-Print hal-01141801, HAL.
    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. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    6. 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.
    7. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2015. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Papers 1504.06094, arXiv.org, revised May 2017.
    8. Hanwu Li & Yongsheng Song, 2021. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2285-2314, December.
    9. Hu, Ying & Tang, Shanjian & Wang, Falei, 2022. "Quadratic G-BSDEs with convex generators and unbounded terminal conditions," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 363-390.
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