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Reflected forward-backward SDEs and obstacle problems with boundary conditions

Ma, Jin and Cvitanić, Jakša (2001) Reflected forward-backward SDEs and obstacle problems with boundary conditions. Journal of Applied Mathematics and Stochastic Analysis, 14 (2). pp. 113-138. ISSN 1048-9533. https://resolver.caltech.edu/CaltechAUTHORS:MAJjamsa01

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Abstract

In this paper we study a class of forward-backward stochastic differential equations with reflecting boundary conditions (FBSDER for short). More precisely, we consider the case in which the forward component of the FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on time and is possibly random. The solvability of such FBSDER is studied in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one-dimensional, then the adapted solution of such FBSDER will give the viscosity solution of a quasilinear variational inequality (obstacle problem) with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1155/S1048953301000090DOIArticle
ORCID:
AuthorORCID
Cvitanić, Jakša0000-0001-6651-3552
Additional Information:© 2008 Ma and Jakša Cvitanić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (Received March, 1999; Revised October, 1999) Research [of J.M. was] supported in part by Office of Naval Research grant N00014-96-1-0262 and NSF grant #DMS-997 1720. Research [by J.C. was] supported in part by Army Research Office grant DAAH 04-95-1-0528.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-96-1-0262
NSFDMS-997 1720
Army Research Office (ARO)DAAH 04-95-1-0528
Subject Keywords:Forward-Backward Stochastic Differential Equations, Quasilinear Variational Inequalities, Viscosity Solutions, American Game Option
Issue or Number:2
Record Number:CaltechAUTHORS:MAJjamsa01
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:MAJjamsa01
Official Citation:Jin Ma and Jakša Cvitanić, “Reflected forward-backward SDEs and obstacle problems with boundary conditions,” Journal of Applied Mathematics and Stochastic Analysis, vol. 14, no. 2, pp. 113-138, 2001. doi:10.1155/S1048953301000090
Usage Policy:Copyright © 2008 Ma and Jakša Cvitanić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ID Code:11813
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:01 Oct 2008 20:36
Last Modified:03 Oct 2019 00:22

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