英文标题：
《Computation of optimal transport and related hedging problems via
penalization and neural networks》
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作者：
Stephan Eckstein and Michael Kupper
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最新提交年份：
2019
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英文摘要：
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, martingale optimal transport, portfolio optimization under uncertainty and generative adversarial networks that showcase the generality and effectiveness of the approach.
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中文摘要：
本文提出了一种通过神经网络解决（多边际，鞅）最优运输及相关问题的广泛适用方法。其核心思想是在对偶公式中惩罚优化问题，并将其简化为有限维问题，这对应于优化具有光滑目标函数的神经网络。我们给出了最优运输、鞅最优运输、不确定性下的投资组合优化和生成对抗网络的数值例子，展示了该方法的通用性和有效性。
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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：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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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