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February 2004 A numerical scheme for BSDEs
Jianfeng Zhang
Ann. Appl. Probab. 14(1): 459-488 (February 2004). DOI: 10.1214/aoap/1075828058


In this paper we propose a numerical scheme for a class of backward stochastic differential equations (BSDEs) with possible path-dependent terminal values. We prove that our scheme converges in the strong $L^2$ sense and derive its rate of convergence. As an intermediate step we prove an $L^2$-type regularity of the solution to such BSDEs. Such a notion of regularity, which can be thought of as the modulus of continuity of the paths in an $L^2$ sense, is new. Some other features of our scheme include the following: (i) both components of the solution are approximated by step processes (i.e., piecewise constant processes); (ii) the regularity requirements on the coefficients are practically "minimum"; (iii) the dimension of the integrals involved in the approximation is independent of the partition size.


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Jianfeng Zhang. "A numerical scheme for BSDEs." Ann. Appl. Probab. 14 (1) 459 - 488, February 2004.


Published: February 2004
First available in Project Euclid: 3 February 2004

zbMATH: 1056.60067
MathSciNet: MR2023027
Digital Object Identifier: 10.1214/aoap/1075828058

Primary: 60H10
Secondary: 65C30

Keywords: $L^\infty$-Lipschitz functionals , $L^2$-regularity , Backward SDEs , step processes

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 1 • February 2004
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