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Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation

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

Published online by Cambridge University Press:  10 November 2015

Jie Yang  and
Weidong Zhao
Jie Yang
Affiliation:
School of Mathematics & Finance Institute, Shandong University, Jinan 250100, China
Weidong Zhao*
Affiliation:
School of Mathematics & Finance Institute, Shandong University, Jinan 250100, China
*
*Corresponding author. Email addresses:yangjie218@yeah.net (J. Yang), wdzhao@sdu.edu.cn (W. Zhao)
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Abstract

Convergence analysis is presented for recently proposed multistep schemes, when applied to a special type of forward-backward stochastic differential equations (FB-SDEs) that arises in finance and stochastic control. The corresponding k-step scheme admits a k-order convergence rate in time, when the exact solution of the forward stochastic differential equation (SDE) is given. Our analysis assumes that the terminal conditions and the FBSDE coefficients are sufficiently regular.

Keywords

Convergence analysismultistep schemesforward-backward stochastic differential equations

MSC classification

Secondary: 60H35: Computational methods for stochastic equations 65C20: Models, numerical methods 60H10: Stochastic ordinary differential equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 4 , November 2015 , pp. 387 - 404
Copyright
Copyright © Global-Science Press 2015 

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