On non-Markovian forward–backward SDEs and backward stochastic PDEs

Jin Ma, Hong Yin and Jianfeng Zhang

Stochastic Processes and their Applications, 2012, vol. 122, issue 12, 3980-4004

Abstract: In this paper, we establish an equivalence relationship between the wellposedness of forward–backward SDEs (FBSDEs) with random coefficients and that of backward stochastic PDEs (BSPDEs). Using the notion of the “decoupling random field”, originally observed in the well-known Four Step Scheme (Ma et al., 1994 [13]) and recently elaborated by Ma et al. (2010) [14], we show that, under certain conditions, the FBSDE is wellposed if and only if this random field is a Sobolev solution to a degenerate quasilinear BSPDE, extending the existing non-linear Feynman–Kac formula to the random coefficient case. Some further properties of the BSPDEs, such as comparison theorem and stability, will also be discussed.

Keywords: Forward–backward stochastic differential equations; Backward stochastic partial differential equations; Nonlinear stochastic Feynman–Kac formula (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (8)

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DOI: 10.1016/j.spa.2012.08.002

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