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Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications

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  • Achref Bachouch
  • C^ome Hur'e
  • Nicolas Langren'e
  • Huyen Pham

Abstract

This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), control learning by hybrid iteration (algorithms Hybrid-Now and Hybrid-LaterQ), on the 100-dimensional nonlinear PDEs examples from [EHJ17] and on quadratic backward stochastic differential equations as in [CR16]. We also performed tests on low-dimension control problems such as an option hedging problem in finance, as well as energy storage problems arising in the valuation of gas storage and in microgrid management. Numerical results and comparisons to quantization-type algorithms Qknn, as an efficient algorithm to numerically solve low-dimensional control problems, are also provided; and some corresponding codes are available on https://github.com/comeh/.

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  • Achref Bachouch & C^ome Hur'e & Nicolas Langren'e & Huyen Pham, 2018. "Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications," Papers 1812.05916, arXiv.org, revised Jan 2020.
    • Handle: RePEc:arx:papers:1812.05916
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    References listed on IDEAS

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    1. Achref Bachouch & Côme Huré & Nicolas Langrené & Huyen Pham, 2019. "Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications," Working Papers hal-01949221, HAL.
    2. Rene Carmona & Michael Ludkovski, 2010. "Valuation of energy storage: an optimal switching approach," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 359-374.
    3. Daniel R. Jiang & Warren B. Powell, 2015. "An Approximate Dynamic Programming Algorithm for Monotone Value Functions," Operations Research, INFORMS, vol. 63(6), pages 1489-1511, December.
    4. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach," Operations Research, INFORMS, vol. 49(3), pages 372-397, June.
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    Cited by:

    1. Nicolas Curin & Michael Kettler & Xi Kleisinger-Yu & Vlatka Komaric & Thomas Krabichler & Josef Teichmann & Hanna Wutte, 2021. "A deep learning model for gas storage optimization," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1021-1037, December.
    2. Achref Bachouch & Côme Huré & Nicolas Langrené & Huyen Pham, 2019. "Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications," Working Papers hal-01949221, HAL.
    3. Simon F'ecamp & Joseph Mikael & Xavier Warin, 2019. "Risk management with machine-learning-based algorithms," Papers 1902.05287, arXiv.org, revised Aug 2020.
    4. Armstrong, Margaret & Langrené, Nicolas & Petter, Renato & Chen, Wen & Petter, Carlos, 2019. "Accounting for tailings dam failures in the valuation of mining projects," Resources Policy, Elsevier, vol. 63(C), pages 1-1.

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