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Strong solutions of forward–backward stochastic differential equations with measurable coefficients

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  • Luo, Peng
  • Menoukeu-Pamen, Olivier
  • Tangpi, Ludovic

Abstract

This paper investigates solvability of fully coupled systems of forward–backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and bounded in the forward process. We crucially use compactness results from the theory of Malliavin calculus to construct strong solutions. Despite the irregularity of the coefficients, the solutions turn out to be differentiable, at least in the Malliavin sense and, as functions of the initial variable, in the Sobolev sense.

Suggested Citation

  • Luo, Peng & Menoukeu-Pamen, Olivier & Tangpi, Ludovic, 2022. "Strong solutions of forward–backward stochastic differential equations with measurable coefficients," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 1-22.
    • Handle: RePEc:eee:spapps:v:144:y:2022:i:c:p:1-22
    DOI: 10.1016/j.spa.2021.10.012
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    References listed on IDEAS

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    1. Issoglio, Elena & Jing, Shuai, 2020. "Forward–backward SDEs with distributional coefficients," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 47-78.
    2. Mikami, Toshio & Thieullen, Michèle, 2006. "Duality theorem for the stochastic optimal control problem," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1815-1835, December.
    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. Antonelli, Fabio & Hamadène, SaI¨d, 2006. "Existence of the solutions of backward-forward SDE's with continuous monotone coefficients," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1559-1569, August.
    5. Horst, Ulrich & Hu, Ying & Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2014. "Forward–backward systems for expected utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1813-1848.
    6. 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.
    7. Delarue, F. & Guatteri, G., 2006. "Weak existence and uniqueness for forward-backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1712-1742, December.
    8. Gregor Heyne & Michael Kupper & Ludovic Tangpi, 2016. "Portfolio Optimization Under Nonlinear Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    9. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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    Cited by:

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