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Solutions and Challenges in Computing FBSDEs with Large Jumps for Dam and Reservoir System Operation

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Computational Science – ICCS 2021 (ICCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12747))

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Abstract

Optimal control of Lévy jump-driven stochastic differential equations plays a central role in management of resource and environment. Problems involving large Lévy jumps are still challenging due to their mathematical and computational complexities. We focus on numerical control of a real-scale dam and reservoir system from the viewpoint of forward-backward stochastic differential equations (FBSDEs): a new mathematical tool in this research area. The problem itself is simple but unique, and involves key challenges common to stochastic systems driven by large Lévy jumps. We firstly present an exactly-solvable linear-quadratic problem and numerically analyze convergence of different numerical schemes. Then, a more realistic problem with a hard constraint of state variables and a more complex objective function is analyzed, demonstrating that the relatively simple schemes perform well.

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Acknowledgements

Kurita Water and Environment Foundation 19B018 and 20K004 and a grant from MLIT Japan for surveys of the landlocked Ayu sweetfish and management of seaweeds in Lake Shinji support this research. The author thanks all the members of mathematical analysis study group in Shimane University for their valuable comments on this research.

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Authors and Affiliations

  1. Graduate School of Natural Science and Technology, Shimane University, Nishikawatsu-cho 1060, Matsue, 690-8504, Japan

    Hidekazu Yoshioka

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  1. Hidekazu Yoshioka
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Correspondence to Hidekazu Yoshioka .

Editor information

Editors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Dieter Kranzlmüller

  3. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  4. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  5. University of Amsterdam, Amsterdam, The Netherlands

    Peter M. A. Sloot

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Yoshioka, H. (2021). Solutions and Challenges in Computing FBSDEs with Large Jumps for Dam and Reservoir System Operation. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12747. Springer, Cham. https://doi.org/10.1007/978-3-030-77980-1_40

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  • DOI: https://doi.org/10.1007/978-3-030-77980-1_40

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77979-5

  • Online ISBN: 978-3-030-77980-1

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