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

## TL;DR

This paper evaluates deep learning algorithms for high-dimensional stochastic control problems, demonstrating their effectiveness through numerical experiments on PDEs, financial, and energy storage applications, with comparisons to existing methods.

## Contribution

It introduces and tests deep neural network algorithms for solving complex stochastic control problems, including high-dimensional PDEs and practical applications, with performance comparisons.

## Key findings

- Deep learning algorithms perform well on 100-dimensional PDEs.
- Algorithms outperform traditional quantization methods in high dimensions.
- Numerical results validate the effectiveness of the proposed methods.

## 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/.