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Deep Learning for Continuous-time Stochastic Control with Jumps

Author

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  • Patrick Cheridito
  • Jean-Loup Dupret
  • Donatien Hainaut

Abstract

In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to approximate the value function. Leveraging a continuous-time version of the dynamic programming principle, we derive two different training objectives based on the Hamilton-Jacobi-Bellman equation, ensuring that the networks capture the underlying stochastic dynamics. Empirical evaluations on different problems illustrate the accuracy and scalability of our approach, demonstrating its effectiveness in solving complex, high-dimensional stochastic control tasks.

Suggested Citation

  • Patrick Cheridito & Jean-Loup Dupret & Donatien Hainaut, 2025. "Deep Learning for Continuous-time Stochastic Control with Jumps," Papers 2505.15602, arXiv.org.
    • Handle: RePEc:arx:papers:2505.15602
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    References listed on IDEAS

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    1. Victor Duarte & Diogo Duarte & Dejanir H Silva, 2024. "Machine Learning for Continuous-Time Finance," The Review of Financial Studies, Society for Financial Studies, vol. 37(11), pages 3217-3271.
    2. Hainaut, Donatien, 2024. "Valuation of guaranteed minimum accumulation benefits (GMABs) with physics-inspired neural networks," Annals of Actuarial Science, Cambridge University Press, vol. 18(2), pages 442-473, July.
    3. Victor Duarte & Diogo Duarte & Dejanir H. Silva, 2024. "Machine Learning for Continuous-Time Finance," CESifo Working Paper Series 10909, CESifo.
    4. Hainaut, Donatien & Akbaraly, Adnane, 2023. "Risk management with Local Least Squares Monte-Carlo," LIDAM Discussion Papers ISBA 2023003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
    6. Hainaut, Donatien & Akbaraly, Adnane, 2023. "Risk management with local least squares Monte Carlo," ASTIN Bulletin, Cambridge University Press, vol. 53(3), pages 489-514, September.
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