Reflected forward-backward SDEs and obstacle problems with boundary conditions. (2001)

• Record Type: Journal Article
• Authors: Ma, Jin; Cvitanić, Jakša
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 14:Number 2(2001)
• Page Start: 113
• Page End: 138
• Publication Date: 2001
• Subjects: forward-backward stochastic differential equations -- quasilinear variational inequalities -- viscosity solutions -- American game option; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953301000090
• Languages: English
• ISSNs: 1048-9533

Abstract

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 .