The Annals of Probability

Anticipated backward stochastic differential equations

Shige Peng and Zhe Yang

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In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.

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Ann. Probab., Volume 37, Number 3 (2009), 877-902.

First available in Project Euclid: 19 June 2009

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Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H20: Stochastic integral equations 93E03: Stochastic systems, general

Anticipated backward stochastic differential equation backward stochastic differential equation adapted process


Peng, Shige; Yang, Zhe. Anticipated backward stochastic differential equations. Ann. Probab. 37 (2009), no. 3, 877--902. doi:10.1214/08-AOP423.

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