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A deep solver for BSDEs with jumps

Author

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  • Alessandro Gnoatto
  • Marco Patacca
  • Athena Picarelli

Abstract

The aim of this work is to propose an extension of the Deep BSDE solver by Han, E, Jentzen (2017) to the case of FBSDEs with jumps. As in the aforementioned solver, starting from a discretized version of the BSDE and parametrizing the (high dimensional) control processes by means of a family of ANNs, the BSDE is viewed as model-based reinforcement learning problem and the ANN parameters are fitted so as to minimize a prescribed loss function. We take into account both finite and infinite jump activity by introducing, in the latter case, an approximation with finitely many jumps of the forward process.

Suggested Citation

  • Alessandro Gnoatto & Marco Patacca & Athena Picarelli, 2022. "A deep solver for BSDEs with jumps," Papers 2211.04349, arXiv.org.
    • Handle: RePEc:arx:papers:2211.04349
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    References listed on IDEAS

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    1. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
    2. Rudiger Frey & Verena Kock, 2021. "Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics," Papers 2109.11403, arXiv.org, revised Sep 2021.
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    Cited by:

    1. Xiangdong Liu & Yu Gu, 2023. "Study of Pricing of High-Dimensional Financial Derivatives Based on Deep Learning," Mathematics, MDPI, vol. 11(12), pages 1-16, June.
    2. Lorenc Kapllani & Long Teng, 2024. "A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations," Papers 2404.08456, arXiv.org.
    3. Emmanuil H. Georgoulis & Antonis Papapantoleon & Costas Smaragdakis, 2024. "A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models," Papers 2401.06740, arXiv.org.

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