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Optimal Error Estimates for a Fully Discrete Euler Scheme for Decoupled Forward Backward Stochastic Differential Equations

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic analysis

Published online by Cambridge University Press:  07 September 2017

Bo Gong  and
Weidong Zhao
Bo Gong*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
Weidong Zhao*
Affiliation:
School of Mathematics & Finance Institute, Shandong University, Jinan, Shandong 250100, China
*
*Corresponding author. Email addresses:[email protected] (B. Gong), [email protected] (W. Zhao)
*Corresponding author. Email addresses:[email protected] (B. Gong), [email protected] (W. Zhao)
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Abstract

In error estimates of various numerical approaches for solving decoupled forward backward stochastic differential equations (FBSDEs), the rate of convergence for one variable is usually less than for the other. Under slightly strengthened smoothness assumptions, we show that the fully discrete Euler scheme admits a first-order rate of convergence for both variables.

Keywords

Forward backward stochastic differential equationsfully discrete schemeerror estimate

MSC classification

Secondary: 60H35: Computational methods for stochastic equations 65C30: Stochastic differential and integral equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 3 , August 2017 , pp. 548 - 565
Copyright
Copyright © Global-Science Press 2017 

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