使用 Deep Q-Learning 求解最优停时问题
Solving optimal stopping problems with Deep Q-Learning
AI总结：
提出基于深度神经网络的强化学习方法求解期权最优停时问题，推导了价格上下界，并扩展至多维和多重停时约束场景。
摘要：
我们提出了一种强化学习（RL）方法，用于对期权类产品的最优行权策略进行建模。我们采用 RL 途径来学习底层停时问题的最优动作价值函数。除了能在任意时间步检索最优 Q 函数外，还能在合约初始时对其进行定价。我们首先讨论了具有单一行权权利的标准设定，随后将该框架扩展到在约束条件下存在多次停时机会的情形。我们提出使用深度神经网络来近似 Q 函数，这不需要像 least-squares Monte Carlo 框架那样指定基函数，并且可扩展至更高维度。我们推导出了由训练好的神经网络得到的期权价格下界，以及由停时问题对偶公式得出的上界，该上界同样可以用 Q 函数表示。我们的方法通过涵盖 swing options 定价的示例进行了说明。
英文摘要：
We propose a reinforcement learning (RL) approach to model optimal exercise strategies for option-type products. We pursue the RL avenue in order to learn the optimal action-value function of the underlying stopping problem. In addition to retrieving the optimal Q-function at any time step, one can also price the contract at inception. We first discuss the standard setting with one exercise right, and later extend this framework to the case of multiple stopping opportunities in the presence of constraints. We propose to approximate the Q-function with a deep neural network, which does not require the specification of basis functions as in the least-squares Monte Carlo framework and is scalable to higher dimensions. We derive a lower bound on the option price obtained from the trained neural network and an upper bound from the dual formulation of the stopping problem, which can also be expressed in terms of the Q-function. Our methodology is illustrated with examples covering the pricing of swing options.
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