A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs
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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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 12 of its 74 references that are in the map. First posted on arXiv 12 Apr 2022.
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References · 12
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- 2019Neural networks-based backward scheme for fully nonlinear PDEscited by 21
- 2019Three algorithms for solving high-dimensional fully-coupled FBSDEs through deep learningcited by 15
- 2020Solving stochastic optimal control problem via stochastic maximum principle with deep learning methodcited by 6
- 2013Optimal control problems of fully coupled FBSDEs and viscosity solutions of Hamilton-Jacobi-Bellman equationscited by 1
- 2017Existence of an Optimal Control for a coupled FBSDE with a non degenerate diffusion coefficientcited by 1
- 2018A global stochastic maximum principle for fully coupled forward-backward stochastic systemscited by 1
- 2018Stochastic maximum principle, dynamic programming principle, and their relationship for fully coupled forward-backward stochastic control systemscited by 1
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