英文标题：
《Deep neural networks algorithms for stochastic control problems on
  finite horizon: numerical applications》
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作者：
Achref Bachouch, C\\^ome Hur\\\'e, Nicolas Langren\\\'e, Huyen Pham
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最新提交年份：
2020
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英文摘要：
  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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中文摘要：
本文介绍了[HPBL18]中介绍的基于深度学习的算法的几个数值应用。使用TensorFlow进行的数值和对比测试说明了我们不同算法的性能，即通过性能迭代进行控制学习（算法NNcontPI和ClassifPI），通过混合迭代进行控制学习（算法hybrid Now和hybrid LaterQ），关于[EHJ17]中的100维非线性偏微分方程示例和[CR16]中的二次倒向随机微分方程。我们还对低维控制问题进行了测试，如金融中的期权对冲问题，以及储气库估值和微电网管理中出现的储能问题。给出了数值结果，并与数值求解低维控制问题的有效算法Qknn进行了比较；上提供了一些相应的代码https://github.com/comeh/.
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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