英文标题：
《Deep Learning for Ranking Response Surfaces with Applications to Optimal
  Stopping Problems》
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作者：
Ruimeng Hu
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最新提交年份：
2020
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英文摘要：
  In this paper, we propose deep learning algorithms for ranking response surfaces, with applications to optimal stopping problems in financial mathematics. The problem of ranking response surfaces is motivated by estimating optimal feedback policy maps in stochastic control problems, aiming to efficiently find the index associated to the minimal response across the entire continuous input space $\\mathcal{X} \\subseteq \\mathbb{R}^d$. By considering points in $\\mathcal{X}$ as pixels and indices of the minimal surfaces as labels, we recast the problem as an image segmentation problem, which assigns a label to every pixel in an image such that pixels with the same label share certain characteristics. This provides an alternative method for efficiently solving the problem instead of using sequential design in our previous work [R. Hu and M. Ludkovski, SIAM/ASA Journal on Uncertainty Quantification, 5 (2017), 212--239].   Deep learning algorithms are scalable, parallel and model-free, i.e., no parametric assumptions needed on the response surfaces. Considering ranking response surfaces as image segmentation allows one to use a broad class of deep neural networks, e.g., UNet, SegNet, DeconvNet, which have been widely applied and numerically proved to possess high accuracy in the field. We also systematically study the dependence of deep learning algorithms on the input data generated on uniform grids or by sequential design sampling, and observe that the performance of deep learning is {\\it not} sensitive to the noise and locations (close to/away from boundaries) of training data. We present a few examples including synthetic ones and the Bermudan option pricing problem to show the efficiency and accuracy of this method.
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中文摘要：
在本文中，我们提出了响应曲面排序的深度学习算法，并将其应用于金融数学中的最优停止问题。响应面排序问题的动机是在随机控制问题中估计最优反馈策略图，目的是在整个连续输入空间$\\数学{X}\\子类Q \\数学{R}^d$中有效地找到与最小响应相关的索引。通过将$\\数学{X}$中的点作为像素，将最小曲面的索引作为标签，我们将该问题重新描述为一个图像分割问题，该问题为图像中的每个像素指定一个标签，使得具有相同标签的像素共享某些特征。这为有效解决问题提供了一种替代方法，而不是在我们之前的工作中使用顺序设计【R.Hu和M.Ludkovski，SIAM/ASA不确定性量化杂志，5（2017），212-239】。深度学习算法具有可扩展性、并行性和无模型性，即响应面无需参数假设。将响应面排序作为图像分割，可以使用一类广泛的深层神经网络，如UNet、SegNet、DECOVNET，这些网络在该领域已得到广泛应用，并经数值证明具有较高的精度。我们还系统地研究了深度学习算法对均匀网格或顺序设计抽样生成的输入数据的依赖性，并观察到深度学习的性能对噪声和训练数据的位置（接近/远离边界）不敏感。我们给出了几个例子，包括合成的例子和百慕大期权定价问题，以证明该方法的有效性和准确性。
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分类信息：

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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一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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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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