Temporal Difference Learning for High-Dimensional PIDEs with Jumps

• URL: http://arxiv.org/abs/2307.02766v2
• Date: Fri, 29 Mar 2024 02:55:22 GMT
• Title: Temporal Difference Learning for High-Dimensional PIDEs with Jumps
• Authors: Liwei Lu, Hailong Guo, Xu Yang, Yi Zhu,
• Abstract summary: We introduce a set of Levy processes and construct a corresponding reinforcement learning model. To simulate the entire process, we use deep neural networks to represent the solutions and non-local terms of the equations. The relative error of the method reaches O(10-3) in 100-dimensional experiments and O(10-4) in one-dimensional pure jump problems.
• Score: 12.734467096363762
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning. We introduce a set of Levy processes and construct a corresponding reinforcement learning model. To simulate the entire process, we use deep neural networks to represent the solutions and non-local terms of the equations. Subsequently, we train the networks using the temporal difference error, termination condition, and properties of the non-local terms as the loss function. The relative error of the method reaches O(10^{-3}) in 100-dimensional experiments and O(10^{-4}) in one-dimensional pure jump problems. Additionally, our method demonstrates the advantages of low computational cost and robustness, making it well-suited for addressing problems with different forms and intensities of jumps.

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