BSDE, path-dependent PDE and nonlinear Feynman-Kac formula

By Shige Peng, Falei Wang. 2011

112 citations recorded by the source corpus.

We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables (t, x) ∈ [0, T] × Rd. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman-Kac formula for a general non-Markovian BSDE. Some main properties of solutions of this new PDEs are also obtained.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ec9289ea5af27e585f6427ed9cf5b039747038f6

How researchers see this paper

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In Finance

1. Jianfeng Zhang
2. Nizar Touzi
3. Ibrahim Ekren
4. Marcel Nutz
5. Frederi G. Viens
6. Cong Wu
7. H. M. Soner
8. Adrien Richou

In Mathematical Physics

1. Jianfeng Zhang
2. Cong Wu
3. Frederi G. Viens
4. Ibrahim Ekren
5. Nizar Touzi
6. Chenchen Mou

Citations in the corpus

• A martingale approach for fractional Brownian motions and related path dependent PDEs (2017, background): “See Peng & Wang [36] for a related result in the Brownian motion framework.”
• Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012, background): “We refer to Peng and Wang [27] for sufficient conditions of existence of classical solutions for more general semilinear PPDEs.”
• Viscosity solutions to parabolic master equations and McKean–Vlasov SDEs with closed-loop controls (2018, methodology): “Proof The proof follows similar arguments as in Peng & Wang [31], which deals with semilinear path dependent PDEs, so we shall only sketch it.”