用深度学习解决高维多重最优停止问题，效率高且可扩展。
Deep Learning for the Multiple Optimal Stopping Problem
- 结合动态规划与神经网络逼近价值函数表面
- 在高维美式篮子期权上误差小，计算效率优于传统方法
- 适合金融工程、量化交易等需多阶段决策的场景
本文提出一种新型深度学习框架，用于求解高维多重最优停止问题。尽管深度学习在单次停止问题上已展现潜力，但多重执行情形涉及复杂递归依赖，仍具挑战。我们通过结合动态规划原理与神经网络对价值函数的逼近来应对。不同于策略搜索方法，该算法显式学习价值曲面。首先研究离散时间问题并分析神经网络训练误差；随后转向连续情形，分析因底层随机过程离散化带来的额外误差。在高维美式篮子期权与非线性效用最大化问题上的数值实验表明，该方法能高效、可扩展地求解多重最优停止问题。
原文摘要 · Abstract (English)
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex recursive dependencies that remain challenging. We address this by combining the Dynamic Programming Principle with neural network approximation of the value function. Unlike policy-search methods, our algorithm explicitly learns the value surface. We first consider the discrete-time problem and analyze neural network training error. We then turn to continuous problems and analyze the additional error due to the discretization of the underlying stochastic processes. Numerical experiments on high-dimensional American basket options and nonlinear utility maximization demonstrate that our method provides an efficient and scalable method for the multiple optimal stopping problem.
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