Strong Stability Preserving Multistep Schemes for Forward Backward Stochastic Differential Equations

In this work, we are concerned with strong stability preserving multistep (SSPM) schemes for forward backward stochastic differential equations (FBSDEs). To this aim, we first perform a comprehensive analysis on a general type of multistep schemes for FBSDEs, based on which we present new sufficient conditions on the coefficients such that the associated schemes are stable and enjoy certain order of consistency. Upon these results, we propose a practical way to design high-order SSPM schemes for FBSDEs. Numerical experiments are carried out to demonstrate the strong stability of our SSPM schemes.

Automated summary

In this work, we focus on strong stability preserving multistep (SSPM) schemes for forward backward stochastic differential equations (FBSDEs). We analyze a general type of multistep schemes for FBSDEs and propose new sufficient conditions on the coefficients for stability and consistency. Based on these results, we present a practical method to design high-order SSPM schemes for FBSDEs. Numerical experiments demonstrate the strong stability of our SSPM schemes.