Second-order numerical schemes for decoupled forward-backward stochastic differential equations with jumps

Weidong Zhao, Wei Zhang, Guannan Zhang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a d-dimensional Brownian motion and an independent compensated Poisson random measure. A semi-discrete scheme is developed for discrete time approximation, which is constituted by a classic scheme for the forward SDE [20, 28] and a novel scheme for the backward SDE. Under some reasonable regularity conditions, we prove that the semi-discrete scheme can achieve second-order convergence in approximating the FBSDEs of interest; and such convergence rate does not require jump-adapted temporal discretization. Next, to add in spatial discretization, a fully discrete scheme is developed by designing accurate quadrature rules for estimating the involved conditional mathematical expectations. Several numerical examples are given to illustrate the effectiveness and the high accuracy of the proposed schemes.

Original languageEnglish
Pages (from-to)213-244
Number of pages32
JournalJournal of Computational Mathematics
Volume35
Issue number2
DOIs
StatePublished - Mar 1 2017

Funding

The authors would like to thank the referees for their valuable comments, which improved much of the quality of the paper. This work is partially supported by the National Natural Science Foundations of China under grant numbers 91130003, 11171189 and 11571206; by Natural Science Foundation of Shandong Province under grant number ZR2011AZ002; by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under contract number ERKJE45; and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory, which is operated by UT-Battelle, LLC, for the U.S. Department of Energy under Contract DE-AC05-00OR22725.

Keywords

  • Backward Kolmogorov equation
  • Decoupled FBSDEs with Lévy jumps
  • Error estimates
  • Nonlinear Feynman-Kac formula
  • Second-order convergence

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