带退出时间的随机控制的策略梯度学习方法及其在股票回购定价中的应用
Policy gradient learning methods for stochastic control with exit time and applications to share repurchase pricing
摘要：
本文研究了无模型下带退出时间的随机控制的策略梯度方法。我们提出了两种类型的学习算法，无论是直接的最优策略，或通过学习交替的价值函数（评论家）和最优控制（演员）。随机策略的使用对于克服梯度计算中与退出时间相关的问题至关重要。我们证明了我们的方法的有效性，通过实施我们的数值方案中的应用程序的股票回购定价问题。我们的研究结果表明，建议的政策梯度方法优于PDE或其他神经网络技术在基于模型的设置。此外，我们的算法足够灵活，可以结合实际的市场条件，例如价格影响或交易成本。
英文摘要：
We develop policy gradients methods for stochastic control with exit time in a model-free setting. We propose two types of algorithms for learning either directly the optimal policy or by learning alternately the value function (critic) and the optimal control (actor). The use of randomized policies is crucial for overcoming notably the issue related to the exit time in the gradient computation. We demonstrate the effectiveness of our approach by implementing our numerical schemes in the application to the problem of share repurchase pricing. Our results show that the proposed policy gradient methods outperform PDE or other neural networks techniques in a model-based setting. Furthermore, our algorithms are flexible enough to incorporate realistic market conditions like e.g. price impact or transaction costs.
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