International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2001 / Article

Open Access

Volume 14 |Article ID 402830 | https://doi.org/10.1155/S1048953301000090

Jin Ma, Jakša Cvitanić, "Reflected forward-backward SDEs and obstacle problems with boundary conditions", International Journal of Stochastic Analysis, vol. 14, Article ID 402830, 26 pages, 2001. https://doi.org/10.1155/S1048953301000090

Reflected forward-backward SDEs and obstacle problems with boundary conditions

Received01 Mar 1999
Revised01 Oct 1999

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.

Copyright © 2001 Hindawi Publishing Corporation. 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.


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