A generalized $\theta$-scheme for solving backward stochastic differential equations

Weidong Zhao; Yang Li; Guannan Zhang

doi:10.3934/dcdsb.2012.17.1585

Article Contents

2012, Volume 17, Issue 5: 1585-1603. Doi: 10.3934/dcdsb.2012.17.1585

This issue Previous Article Impact of $\alpha$-stable Lévy noise on the Stommel model for the thermohaline circulation Next Article

A generalized $\theta$-scheme for solving backward stochastic differential equations

1.
School of Mathematics, Shandong University, Jinan, Shandong
2.
Department of Scientiﬁc Computing, Florida State University, Tallahassee, FL 32306

Received: July 31, 2011

Revised: October 31, 2011

Published: June 2012

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Abstract

In this paper we propose a new type of $\theta$-scheme with four parameters ($\{\theta_i\}_{i=1}^4$) for solving the backward stochastic differential equation $-dy_t=f(t,y_t,z_t) dt - z_t dW_t$. We rigorously prove some error estimates for the proposed scheme, and in particular, we show that accuracy of the scheme can be high by choosing proper parameters. Various numerical examples are also presented to verify the theoretical results.

Keywords:

Backward stochastic differential equations,
$\theta$-scheme,
error estimate,
second order,
numerical tests.

Mathematics Subject Classification: Primary: 60H35, 65C20; Secondary: 65C30.

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