A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911994679918592 |
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| author | Ji, Shaolin Peng, Shige Peng, Ying Zhang, Xichuan |
| author_facet | Ji, Shaolin Peng, Shige Peng, Ying Zhang, Xichuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05796 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs Ji, Shaolin Peng, Shige Peng, Ying Zhang, Xichuan Optimization and Control Artificial Intelligence 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. |
| title | A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs |
| topic | Optimization and Control Artificial Intelligence |
| url | https://arxiv.org/abs/2204.05796 |