Issoglio, E orcid.org/0000-0003-3035-2712 and Jing, S (2020) Forward–backward SDEs with distributional coefficients. Stochastic Processes and their Applications, 130 (1). pp. 47-78. ISSN 0304-4149
Abstract
Forward–backward stochastic differential equations (FBSDEs) have attracted significant attention since they were introduced, 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 solution and show its existence and in certain cases its uniqueness. Moreover we establish a link with PDE theory via a non-linear Feynman–Kac formula. The associated semi-linear parabolic PDE is the same for both FBSDEs, also involves distributional coefficients and has not previously been investigated.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Elsevier B.V. All rights reserved. This is an author produced version of a paper published in Stochastic Processes and their Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Forward–backward stochastic differential equations; Distributional coefficients; Non-linear Feynman–Kac formula; Weak solutions; Virtual solutions; Mild solutions; Sobolev spaces; Singular FBSDEs; Singular PDEs |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Jan 2019 13:43 |
Last Modified: | 14 Jan 2020 01:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.spa.2019.01.001 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:140760 |