用深度强化学习实现连续时间最优停止，精度更高且计算更快。
Continuous-time Optimal Stopping through Deep Reinforcement Learning
- 通过自适应神经网络学习时空联合决策边界，支持任意细粒度时间点停止单元
- 在美式期权定价中逼近上界，优于现有巴尔莫丹求解器
- 自适应采样聚焦停止边界，显著提升训练效率，适合金融衍生品定价
基于模拟的最优停止问题求解方法需对停止决策进行离散化。传统动态规划下，粗略的执行网格会显著低估最优期望收益，而极细网格则导致向后递推中的近似误差累积。为突破此限制，我们提出一种受强化学习启发的新算法——CARLOS（连续时间自适应强化学习最优停止）。该算法利用聚合深度神经网络（ADNN）学习时空联合决策边界。从粗略时间网格出发，逐步增加停止机会频率，同时并行训练ADNN以精炼其时序价值估计。此外，设计了自适应采样策略，将训练重点逐渐集中于停止边界附近。基准测试显示，CARLOS在定价精度上超越现有巴尔莫丹求解器，逼近美式期权上界，且相较非强化学习方法具有更高的计算效率。
原文摘要 · Abstract (English)
Simulation based solvers for optimal stopping problems must discretize the stopping decision. Under classical dynamic programming, a coarse exercise grid with only a few stopping opportunities can materially undervalue the optimal expected reward, whereas on a very fine grid, approximation errors accumulate through the backward recursion. To remove this limitation, we develop a new reinforcement-learning inspired algorithm that enables us to learn the exercise rule at arbitrarily fine time resolution. Our CARLOS (Continuous-time Adaptive Reinforcement Learning for Optimal Stopping) algorithm utilizes an aggregate deep neural network (ADNN) to learn a joint space-time decision boundary. Starting from a coarse time grid, we progressively increase the frequency of stopping opportunities, while in parallel training the ADNN to refine its timing-value estimates. We moreover design an adaptive sampling strategy that gradually concentrates training effort near the stopping boundary. Benchmarked results show that CARLOS delivers higher prices than existing Bermudan solvers, approaching the American upper bound, and achieves high computational efficiency relative to non-RL comparators.
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