Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Numerical Applications

Achref Bachouch (), Côme Huré (), Nicolas Langrené () and Huyên Pham ()
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Achref Bachouch: Mälardalen University
Côme Huré: LPSM, University Paris Diderot
Nicolas Langrené: RiskLab Australia
Huyên Pham: LPSM, University Paris Diderot

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 1, 143-178

Abstract: Abstract This paper presents several numerical applications of deep learning-based algorithms for discrete-time stochastic control problems in finite time horizon that have been introduced in Huré et al. (2018). 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 Weinan et al. (2017) and on quadratic backward stochastic differential equations as in Chassagneux and Richou (2016). 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.

Keywords: Deep learning; Policy learning; Performance iteration; Value iteration; Monte Carlo; Quantization (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s11009-019-09767-9

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