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Existence and Uniqueness of Solutions for Multi-dimensional Reflected Backward Stochastic Differential Equations with Diagonally Quadratic Generators

Author

Listed:
  • Yuyang Chen

    (Shanghai Jiao Tong University)

  • Peng Luo

    (Shanghai Jiao Tong University)

Abstract

In this paper, we study multi-dimensional reflected backward stochastic differential equations (BSDEs) with diagonally quadratic generators. Using the comparison theorem for diagonally quadratic BSDEs established recently in Luo (Disc Contin Dyn Syst 41(6):2543–2557, 2021), we obtain the existence and uniqueness of a solution by a penalization method. Moreover, we provide a comparison theorem.

Suggested Citation

  • Yuyang Chen & Peng Luo, 2023. "Existence and Uniqueness of Solutions for Multi-dimensional Reflected Backward Stochastic Differential Equations with Diagonally Quadratic Generators," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1698-1719, September.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01224-7
    DOI: 10.1007/s10959-022-01224-7
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    References listed on IDEAS

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    1. Hu, Ying & Tang, Shanjian, 2016. "Multi-dimensional backward stochastic differential equations of diagonally quadratic generators," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1066-1086.
    2. Matoussi, Anis, 1997. "Reflected solutions of backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 347-354, June.
    3. Xu, Mingyu, 2008. "Backward stochastic differential equations with reflection and weak assumptions on the coefficients," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 968-980, June.
    4. Xing, Hao & Žitković, Gordan, 2018. "A class of globally solvable Markovian quadratic BSDE systems and applications," LSE Research Online Documents on Economics 73440, London School of Economics and Political Science, LSE Library.
    5. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
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