现实期权模型中的强化学习
Reinforcement Learning in Real Option Models
AI总结：
本文提出了一种熵正则化的强化学习方法，用于解决现实期权模型中的最优停止问题，通过平衡探索与利用，提高了在不确定性下的停止决策性能。
摘要：
我们研究了一种熵正则化的强化学习（RL）方法，用于最优停止问题，这受到现实期权模型的启发。经典停止规则是严格且非随机化的，限制了强化学习设置中的自然探索。为了解决这个问题，我们引入熵正则化，允许随机停止策略，以平衡利用和探索。我们推导了正则化问题的显式解析解，并证明了相应的自由边界收敛到经典停止阈值，当熵消失时。正则化问题可以自然地表述为一个奇异随机控制问题。基于这一结构，我们提出了基于模型和无模型的策略迭代算法来学习最优边界。无模型方法不依赖系统动态的知识，仅使用来自随机环境的轨迹。我们建立了收敛保证并展示了强大的数值性能。这一框架为在不确定性下的数据驱动停止问题提供了一种系统且可处理的方法。
英文摘要：
We investigate an entropy-regularized reinforcement learning (RL) approach to optimal stopping problems motivated by real option models. Classical stopping rules are strict and non-randomized, limiting natural exploration in RL settings. To address this, we introduce entropy regularization, allowing randomized stopping policies that balance exploitation and exploration. We derive an explicit analytical solution to the regularized problem and prove convergence of the associated free boundary to the classical stopping threshold as the entropy vanishes. The regularized problem admits a natural formulation as a singular stochastic control problem. Building on this structure, we propose both model-based and model-free policy iteration algorithms to learn the optimal boundary. The model-free method operates without knowledge of system dynamics, using only trajectories from the stochastic environment. We establish convergence guarantees and illustrate strong numerical performance. This framework provides a principled and tractable approach for data-driven stopping problems under uncertainty.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
