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Reflected backward stochastic differential equation driven by G-Brownian motion with an upper obstacle

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  • Li, Hanwu
  • Peng, Shige

Abstract

In this paper, we study the reflected backward stochastic differential equation driven by G-Brownian motion (reflected 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, 2020. "Reflected backward stochastic differential equation driven by G-Brownian motion with an upper obstacle," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6556-6579.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6556-6579
    DOI: 10.1016/j.spa.2020.06.002
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    References listed on IDEAS

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    1. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    2. 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.
    3. 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.
    4. Anis Matoussi & Lambert Piozin & Dylan Possamai, 2012. "Second-order BSDEs with general reflection and game options under uncertainty," Papers 1212.0476, arXiv.org, revised Jan 2014.
    5. 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.
    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. 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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    Cited by:

    1. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.

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