Journal of Scientific Computing

, Volume 69, Issue 2, pp 651–672

Multistep Schemes for Forward Backward Stochastic Differential Equations with Jumps


DOI: 10.1007/s10915-016-0212-y

Cite this article as:
Fu, Y., Zhao, W. & Zhou, T. J Sci Comput (2016) 69: 651. doi:10.1007/s10915-016-0212-y


In this work, we are concerned with multistep schemes for solving forward backward stochastic differential equations with jumps. The proposed multistep schemes admit many advantages. First of all, motivated by the local property of jump diffusion processes, the Euler method is used to solve the associated forward stochastic differential equation with jump, which reduce dramatically the entire computational complexity, however, the quantities of interests in the backward stochastic differential equations (with jump) are still of high order rate of convergence. Secondly, in each time step, only one jump is involved in the computational procedure, which again reduces dramatically the computational complexity. Finally, the method applies easily to partial-integral differential equations (and some nonlocal PDE models), by using the generalized Feynman–Kac formula. Several numerical experiments are presented to demonstrate the effectiveness of the proposed multistep schemes.


Multistep scheme Jump-diffusion process Forward backward stochastic differential equation with jumps 

Mathematics Subject Classification

60H35 65C20 

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Mathematics and Institute of FinanceShandong UniversityJinanChina
  2. 2.LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina