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Nonlinear Feynman-Kac formula and discrete-functional-type BSDEs with continuous coefficients

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  • Hu, Ying
  • Ma, JinJin

Abstract

In this paper, we study a class of multi-dimensional backward stochastic differential equations (BSDEs, for short) in which the terminal values and the generators are allowed to be "discrete-functionals" of a forward diffusion. We first establish some new types of Feynman-Kac formulas related to such BSDEs under various regularity conditions, and then we prove that under only bounded continuous assumptions on the generators, the adapted solution to such BSDEs does exist. Our result on the existence of the solutions to higher-dimensional BSDEs is new, and our representation theorem is the first step towards the long-standing "functional-type" Feynman-Kac formula.

Suggested Citation

  • Hu, Ying & Ma, JinJin, 2004. "Nonlinear Feynman-Kac formula and discrete-functional-type BSDEs with continuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 23-51, July.
    • Handle: RePEc:eee:spapps:v:112:y:2004:i:1:p:23-51
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    1. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    2. 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.
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    Cited by:

    1. Wang, Tianxiao & Yong, Jiongmin, 2019. "Backward stochastic Volterra integral equations—Representation of adapted solutions," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4926-4964.
    2. Ma, Jin & Yin, Hong & Zhang, Jianfeng, 2012. "On non-Markovian forward–backward SDEs and backward stochastic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3980-4004.
    3. Geiss, Christel & Geiss, Stefan & Gobet, Emmanuel, 2012. "Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2078-2116.
    4. 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.

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