Forward-backward SDEs with distributional coefficients
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Publication:2289778
DOI10.1016/J.SPA.2019.01.001zbMATH Open1443.60062arXiv1605.01558OpenAlexW2964029487WikidataQ128564656 ScholiaQ128564656MaRDI QIDQ2289778
Author name not available (Why is that?)
Publication date: 24 January 2020
Published in: (Search for Journal in Brave)
Abstract: Forward-backward stochastic differential equations (FBSDEs) have attracted significant attention since they were introduced almost 30 years ago, due to their wide range of applications, from solving non-linear PDEs to pricing American-type options. Here, we consider two new classes of multidimensional FBSDEs with distributional coefficients (elements of a Sobolev space with negative order). We introduce a suitable notion of a solution, show existence and uniqueness of a strong solution of the first FBSDE, and weak existence for the second. We establish a link with PDE theory via a nonlinear Feynman-Kac representation formula. The associated semi-linear second order parabolic PDE is the same for both FBSDEs, also involves distributional coefficients and has not previously been investigated; our analysis uses mild solutions, Sobolev spaces and semigroup theory.
Full work available at URL: https://arxiv.org/abs/1605.01558
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