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Approximate Solvability of Forward—Backward Stochastic Differential Equations

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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 solvabilityof 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.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University,West Lafayette, IN 47907-1395, USA majin@math.purdue.edu, USA

    J. Ma

  2. Laboratory of Mathematics for Nonlinear Sciences, Department of Mathematics, and Institute of Mathematical Finance, Fudan University,Shanghai 200433, People's Republic of China, People's Republic of China

    J. Yong

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  1. J. Ma
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  2. J. Yong
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Accepted 17 April 2001. Online publication 14 August 2001.

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Ma, J., Yong, J. Approximate Solvability of Forward—Backward Stochastic Differential Equations. Appl Math Optim 45, 1–22 (2002). https://doi.org/10.1007/s00245-001-0025-7

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  • DOI: https://doi.org/10.1007/s00245-001-0025-7

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