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Global Well-posedness of Non-Markovian Multidimensional Superquadratic BSDE

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  • Kihun Nam

Abstract

(Working Paper) Using a purely probabilistic argument, we prove the global well-posedness of multidimensional superquadratic backward stochastic differential equations (BSDEs) without Markovian assumption. The key technique is the interplay between the local well-posedness of fully coupled path-dependent forward backward stochastic differential equations (FBSDEs) and backward iterations of the superquadratic BSDE. The superquadratic BSDE studied in this article includes quadratic BSDEs appear in stochastic differential game and price impact model. We also study the well-posedness of superquadratic FBSDEs and FBSDEs with measurable coefficients using the corresponding BSDE results. Our result also provides the well-posedness of a system of path-dependent quasilinear partial differential equations where the nonlinearity has superquadratic growth in the gradient of the solution.

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  • Kihun Nam, 2019. "Global Well-posedness of Non-Markovian Multidimensional Superquadratic BSDE," Papers 1912.03692, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:1912.03692
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    1. 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.
    2. 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.
    3. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, 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. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    6. 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.
    7. Briand, Philippe & Elie, Romuald, 2013. "A simple constructive approach to quadratic BSDEs with or without delay," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2921-2939.
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    Cited by:

    1. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.

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