American options allow early exercise, which yields an additional challenge – besides the weights of each option – when optimizing a portfolio of American options. In this work, we construct strategies for an American option portfolio by exercising options at optimal timings with optimal weights determined concurrently. To model such portfolios, a reinforcement learning (Q-learning) algorithm is proposed, combining an iterative progressive hedging method and a quadratic approximation to Q-values by regression. By means of Monte Carlo simulation and empirical experiments, using data from the SPY options market, we evaluate the quality of our algorithms and examine their performance under various investment assumptions, such as different portfolio settings and distributions of the underlying asset returns. With discretized timings, our strategies work better in a relatively long time horizon and when the portfolio is hedged using the underlying instrument. Due to the highly leveraged and risky nature of our strategies, overly risk-averse investors are proved unsuitable for such investment opportunities.

中文翻译：

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美式期权的投资组合优化

美式期权允许提前行使，这在优化美式期权组合时会产生额外的挑战——除了每个期权的权重。在这项工作中，我们通过在最佳时间行使期权并同时确定最佳权重来构建美式期权投资组合的策略。为了对此类投资组合建模，提出了一种强化学习 (Q-learning) 算法，该算法将迭代渐进对冲方法和通过回归对 Q 值的二次近似相结合。通过蒙特卡罗模拟和实证实验，使用来自 SPY 期权市场的数据，我们评估了我们算法的质量并检查了它们在各种投资假设下的表现，例如不同的投资组合设置和基础资产回报的分布。随着离散时间，我们的策略在相对较长的时间范围内以及使用基础工具对投资组合进行对冲时效果更好。由于我们策略的高杠杆和风险性质，过度规避风险的投资者被证明不适合此类投资机会。