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Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation

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  • Hu, Ying
  • Lin, Yiqing
  • Soumana Hima, Abdoulaye

Abstract

In this paper, we consider backward stochastic differential equations driven by G-Brownian motion (GBSDEs) under quadratic assumptions on coefficients. We prove the existence and uniqueness of solution for such equations. On the one hand, a priori estimates are obtained by applying the Girsanov type theorem in the G-framework, from which we deduce the uniqueness. On the other hand, to prove the existence of solutions, we first construct solutions for discrete GBSDEs by solving corresponding fully nonlinear PDEs, and then approximate solutions for general quadratic GBSDEs in Banach spaces.

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  • Hu, Ying & Lin, Yiqing & Soumana Hima, Abdoulaye, 2018. "Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3724-3750.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:11:p:3724-3750
    DOI: 10.1016/j.spa.2017.12.004
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. He, Wei, 2024. "Multi-dimensional mean-reflected BSDEs driven by G-Brownian motion with time-varying non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 206(C).
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    6. Shengqiu Sun, 2022. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Coefficients in (y, z)," Journal of Theoretical Probability, Springer, vol. 35(1), pages 370-409, March.

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