The Annals of Applied Probability

Numerical methods for forward-backward stochastic differential equations

Jim Douglas, Jr., Jin Ma, and Philip Protter

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Abstract

In this paper we study numerical methods to approximate the adapted solutions to a class of forward-backward stochastic differential equations (FBSDE's). The almost sure uniform convergence as well as the weak convergence of the scheme are proved, and the rate of convergence is proved to be as good as the approximation for the corresponding forward SDE. The idea of the approximation is based on the four step scheme for solving such an FBSDE, developed by Ma, Protter and Yong. For the PDE part, the combined characteristics and finite difference method is used, while for the forward SDE part, we use the first order Euler scheme.

Article information

Source
Ann. Appl. Probab., Volume 6, Number 3 (1996), 940-968.

Dates
First available in Project Euclid: 18 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1034968235

Digital Object Identifier
doi:10.1214/aoap/1034968235

Mathematical Reviews number (MathSciNet)
MR1410123

Zentralblatt MATH identifier
0861.65131

Subjects
Primary: 65U05
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 65M06: Finite difference methods 65M25: Method of characteristics

Keywords
Forward-backward stochastic differential equations quasilinear parabolic equations combined characteristics and finite difference method Euler's scheme weak convergence

Citation

Douglas, Jim; Ma, Jin; Protter, Philip. Numerical methods for forward-backward stochastic differential equations. Ann. Appl. Probab. 6 (1996), no. 3, 940--968. doi:10.1214/aoap/1034968235. https://projecteuclid.org/euclid.aoap/1034968235


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  • WEST LAFAy ETTE, INDIANA 47907-1395 E-MAIL: douglas@math.purdue.edu majin@math.purdue.edu protter@math.purdue.edu