Numerical Solution for Backward SDEs : A Regression Later Algorithm

This paper deals with the numerical approximation of backward stochastic differential equations (BSDEs). We propose a new algorithm which is based on the regression later approach. Under some regularity assumptions, the solution of a forward backward stochastic differential equation (FBSDE) can be represented by the solution of a regular quasi-linear parabolic partial differential equation (PDE). On this basis, we have developed a probabilistic numerical regression called regression later algorithm based on the least squares Monte Carlo method and the previous connection between the quasi-linear parabolic partial differential equation and the FBSDE. The proposed algorithm yields good convergence results in practice. We will introduce briefly the theory of BSDEs, provide some general background on their studies and review the classical backward Euler-Maruyama scheme. Subsequently, we will describe the regression later algorithm, in further detail the algorithm and derive a convergence result. Finally, we will provides two numerical experiments to test the performance of the algorithm