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Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations***

Published online by Cambridge University Press:  24 August 2010

Shige Peng  and
Mingyu Xu
Shige Peng
Affiliation:
School of Mathematics and System Science, Shandong University, 250100 Jinan, P.R. China. peng@sdu.edu.cn. Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, CAS (No. 2008DP173182), P.R. China. xumy@amss.ac.cn.
Mingyu Xu
Affiliation:
Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, CAS (No. 2008DP173182), P.R. China. xumy@amss.ac.cn. Department of Financial Mathematics and Control science, School of Mathematical Science, Fudan University, 200433 Shanghai, P.R. China.
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Abstract

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

Keywords

Backward stochastic differential equationsreflected stochastic differential equations with one barriernumerical algorithmnumerical simulation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 2 , March 2011 , pp. 335 - 360
Copyright
© EDP Sciences, SMAI, 2010

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