Error estimates of the $\theta$-scheme for backward stochastic differentialequations

By Weidong Zhao, Jin-lei Wang, Shige Peng. 2009

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In this paper, we study the error estimate of the $\theta$-scheme for the backward stochastic differential equation $y_t=\varphi(W_T)+\int_t^Tf(s,y_s)ds-\int_t^Tz_sdW_s$. We show that this scheme is of first-order convergence in $y$ for general $\theta$. In particular, for the case of $\theta=\frac{1}{2}$ (i.e., the Crank-Nicolson scheme), we prove that this scheme is of second-order convergence in $y$ and first-order in $z$. Some numerical examples are also given to validate our theoretical results.

Subfields: Demography, Finance

View Paper: https://www.semanticscholar.org/paper/3079fc2a41f8c45f065a47bad5f6cbbb451a1e64