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. doi:10.1155/S1048953301000090. 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.
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| 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. | ||||||||
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| Subject Keywords: | Forward-Backward Stochastic Differential Equations, Quasilinear Variational Inequalities, Viscosity Solutions, American Game Option | ||||||||
| Issue or Number: | 2 | ||||||||
| DOI: | 10.1155/S1048953301000090 | ||||||||
| 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: | 08 Nov 2021 22:02 |
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