Approximate Solvability of Forward—Backward Stochastic Differential Equations |
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| Authors: | J Ma J Yong |
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| Institution: | (1) Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, USA majin@math.purdue.edu, US;(2) Laboratory of Mathematics for Nonlinear Sciences, Department of Mathematics, and Institute of Mathematical Finance, Fudan University, Shanghai 200433, People's Republic of China, CN |
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| Abstract: | The solvability of forward—backward stochastic differential equations (FBSDEs for short) has been studied extensively in
recent years. To guarantee the existence and uniqueness of adapted solutions, many different conditions, some quite restrictive,
have been imposed. In this paper we propose a new notion: the approximate solvability of FBSDEs, based on the method of optimal control introduced in our primary work 15]. The approximate solvability of a
class of FBSDEs is shown under mild conditions; and a general scheme for constructing approximate adapted solutions is proposed.
Accepted 17 April 2001. Online publication 14 August 2001. |
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| Keywords: | , Forward—,backward stochastic differential equation, Approximate solvability, Approximate adapted solution, Nodal,,,,,set, AMS Classification, 60H15, 35R60, 34F05, 93E20, |
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