Error Estimates of the Crank-Nicolson Scheme for Solving Backward Stochastic Differential Equations

Error Estimates of the Crank-Nicolson Scheme for Solving Backward Stochastic Differential Equations

Year:    2013

International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 876–898

Abstract

In this paper, we study error estimates of a special $\theta$-scheme — the Crank-Nicolson scheme proposed in [25] for solving the backward stochastic differential equation with a general generator, $-dy_t = f(t, y_t, z_t)dt-z_tdW_t$. We rigorously prove that under some reasonable regularity conditions on $\varphi$ and $f$, this scheme is second-order accurate for solving both $y_t$ and $z_t$ when the errors are measured in the $L^p (p \geq 1)$ norm.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2013-IJNAM-601

International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 876–898

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Backward stochastic differential equations Crank-Nicolson scheme $\theta$-scheme error estimate.