标题：NEW KINDS OF HIGH-ORDER MULTISTEP SCHEMES FOR COUPLED FORWARD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
作者：Zhao, Weidong; Fu, Yu; Zhou, Tao
作者机构：[Zhao, Weidong; Fu, Yu] Shandong Univ, Sch Math, Jinan 250100, Peoples R China.; [Zhao, Weidong; Fu, Yu] Shandong Univ, Finance Inst, Jinan 250100, 更多
通讯作者地址：[Zhao, WD]Shandong Univ, Sch Math, Jinan 250100, Peoples R China.
来源：SIAM JOURNAL ON SCIENTIFIC COMPUTING
关键词：high-order; multistep scheme; diffusion process; Euler method; coupled; Markovian forward backward stochastic differential equations
摘要：In this work, we are concerned with the high-order numerical methods for coupled forward-backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we derive two reference ordinary differential equations (ODEs) from the backward SDE, which contain the conditional expectations and their derivatives. Then, our high-order multistep schemes are obtained by carefully approximating the conditional expectations and the derivatives, in the reference ODEs. Motivated by the local property of the generator of diffusion processes, the Euler method is used to solve the forward SDE; however, it is noticed that the numerical solution of the backward SDE is still of high-order accuracy. Such results are obviously promising: on one hand, the use of the Euler method (for the forward SDE) can dramatically simplify the entire computational scheme, and on the other hand, one might be only interested in the solution of the backward SDE in many real applications such as option pricing. Several numerical experiments are presented to demonstrate the effectiveness of the numerical method.