# A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs

arXiv: https://arxiv.org/abs/2204.05796 · HTML: https://mlsanity.com/paper/2204.05796/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 74 references that are in the map.
- First posted on arXiv 12 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations](https://mlsanity.com/paper/1709.05963/) (2017)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Convergence of the Deep BSDE Method for Coupled FBSDEs](https://mlsanity.com/paper/1811.01165/) (2018)
- [Neural networks-based backward scheme for fully nonlinear PDEs](https://mlsanity.com/paper/1908.00412/) (2019)
- [Three algorithms for solving high-dimensional fully-coupled FBSDEs through deep learning](https://mlsanity.com/paper/1907.05327/) (2019)
- [Solving stochastic optimal control problem via stochastic maximum principle with deep learning method](https://mlsanity.com/paper/2007.02227/) (2020)
- [Optimal control problems of fully coupled FBSDEs and viscosity solutions of Hamilton-Jacobi-Bellman equations](https://mlsanity.com/paper/1302.0935/) (2013)
- [Existence of an Optimal Control for a coupled FBSDE with a non degenerate diffusion coefficient](https://mlsanity.com/paper/1702.00194/) (2017)
- [A global stochastic maximum principle for fully coupled forward-backward stochastic systems](https://mlsanity.com/paper/1803.02109/) (2018)
- [Stochastic maximum principle, dynamic programming principle, and their relationship for fully coupled forward-backward stochastic control systems](https://mlsanity.com/paper/1803.06804/) (2018)

## Built on by (most cited first, 2 of 2)

- [A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations](https://mlsanity.com/paper/2404.08456/) (2024)
- [Deep Generative Modeling with Backward Stochastic Differential Equations](https://mlsanity.com/paper/2304.04049/) (2023)

## Abstract (arXiv)

In this paper,we mainly focus on the numerical solution of high-dimensional stochastic optimal control problem driven by fully-coupled forward-backward stochastic differential equations (FBSDEs in short) through deep learning. We first transform the problem into a stochastic Stackelberg differential game problem (leader-follower problem), then a bi-level optimization method is developed where the leader's cost functional and the follower's cost functional are optimized alternatively via deep neural networks. As for the numerical results, we compute two examples of the investment-consumption problem solved through stochastic recursive utility models, and the results of both examples demonstrate the effectiveness of our proposed algorithm.