熵正则化美式期权的单调极限方法
A Monotone Limit Approach to Entropy-Regularized American Options
AI总结：
本文提出了一种基于Snell包络和反射反向随机微分方程的完全概率框架，用于熵正则化美式期权的单调极限方法，并通过数值实验验证了其有效性。
摘要：
近年来，连续时间最优停止问题的进步主要由熵正则化随机停止问题的公式化所驱动，大多数现有方法依赖于偏微分方程方法。在本文中，我们提出了一种基于Doob-Meyer-Mertens分解的Snell包络的完全概率框架，并通过反射反向随机微分方程对其进行表示。我们引入了一种熵正则化惩罚方案，从而得到价值函数的单调近似，并在适当的正则性假设下建立了显式收敛率。此外，我们开发了一种基于线性反向随机微分方程的策略改进算法，并通过一个简单的数值实验展示了其在美式最大看涨期权中的表现。
英文摘要：
Recent advances in continuous-time optimal stopping have been driven by entropy-regularized formulations of randomized stopping problems, with most existing approaches relying on partial differential equation methods. In this paper, we propose a fully probabilistic framework based on the Doob-Meyer-Mertens decomposition of the Snell envelope and its representation through reflected backward stochastic differential equations. We introduce an entropy-regularized penalization scheme yielding a monotone approximation of the value function and establish explicit convergence rates under suitable regularity assumptions. In addition, we develop a policy improvement algorithm based on linear backward stochastic differential equations and illustrate its performance through a simple numerical experiment for an American-style max call option
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。
