Splitting Schemes for Second-Order Backward Stochastic Differential Equations

Abstract

In this work, we focus on splitting methods for solving second-order backward stochastic differential equations (2BSDEs). By splitting the original $d$-dimensional 2BSDEs into $d$ 2BSDEs and approximating these split 2BSDEs, we derive the splitting schemes that only require one-dimensional approximations to evaluate the conditional mathematical expectations. Combining the Sinc quadrature rule to approximate the conditional expectations, we further propose the first-order fully discrete splitting schemes. Numerical tests are presented to show the capacity of the schemes.