The Annals of Applied Probability

A numerical scheme for BSDEs

Jianfeng Zhang

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 14, Number 1 (2004), 459-488.

Dates
First available in Project Euclid: 3 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1075828058

Digital Object Identifier
doi:10.1214/aoap/1075828058

Mathematical Reviews number (MathSciNet)
MR2023027

Zentralblatt MATH identifier
1056.60067

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 65C30: Stochastic differential and integral equations

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

Citation

Zhang, Jianfeng. A numerical scheme for BSDEs. Ann. Appl. Probab. 14 (2004), no. 1, 459--488. doi:10.1214/aoap/1075828058. https://projecteuclid.org/euclid.aoap/1075828058


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