Time-reversal solution of BSDEs in stochastic optimal control: a linear quadratic study

TL;DR

This paper compares two numerical methods for solving BSDEs in stochastic optimal control, demonstrating that the time-reversal approach offers superior accuracy and efficiency in linear-quadratic cases.

Contribution

It introduces and evaluates a time-reversal method for BSDEs, showing its advantages over least-squares Monte-Carlo in linear-quadratic stochastic control problems.

Findings

Time-reversal method outperforms LSMC in accuracy

TR approach is more efficient computationally

Analytical solutions validate numerical results

Abstract

This paper addresses the numerical solution of backward stochastic differential equations (BSDEs) arising in stochastic optimal control. Specifically, we investigate two BSDEs: one derived from the Hamilton-Jacobi-Bellman equation and the other from the stochastic maximum principle. For both formulations, we analyze and compare two numerical methods. The first utilizes the least-squares Monte-Carlo (LSMC) approach for approximating conditional expectations, while the second leverages a time-reversal (TR) of diffusion processes. Although both methods extend to nonlinear settings, our focus is on the linear-quadratic case, where analytical solutions provide a benchmark. Numerical results demonstrate the superior accuracy and efficiency of the TR approach across both BSDE representations, highlighting its potential for broader applications in stochastic control.