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arXiv · 2410.04615

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

Yuhang Mei·Amirhossein Taghvaei
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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.

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Yuhang Mei, Amirhossein Taghvaei. 2024-10-06. Time-reversal solution of BSDEs in stochastic optimal control: a linear quadratic study. https://arxiv.org/abs/2410.04615

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