Regression Monte Carlo for Impulse Control
Regression Monte Carlo for Impulse Control
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DOI：
10.5802/msia.18
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发表时间：
2022-03
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通讯作者：
M. Ludkovski
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作者：
M. Ludkovski
我本着蒙特卡罗回归的精神开发了一种用于随机脉冲控制的数值算法，以实现最佳停止。该方法包括为连续函数生成统计代理（也称为函数逼近器）。通过模拟状态轨迹的经验回归对代理进行递归训练。同时，相同的代理用于学习表征最佳脉冲量的干预函数。我讨论了该任务的适当代理类型，以及训练集的选择。森林轮作和不可逆投资的案例研究说明了数值方案并强调了其灵活性和可扩展性。 \texttt{R} 中的实现作为发布在 GitHub 上的公开可用包提供。
I develop a numerical algorithm for stochastic impulse control in the spirit of Regression Monte Carlo for optimal stopping. The approach consists in generating statistical surrogates (aka functional approximators) for the continuation function. The surrogates are recursively trained by empirical regression over simulated state trajectories. In parallel, the same surrogates are used to learn the intervention function characterizing the optimal impulse amounts. I discuss appropriate surrogate types for this task, as well as the choice of training sets. Case studies from forest rotation and irreversible investment illustrate the numerical scheme and highlight its flexibility and extensibility. Implementation in \texttt{R} is provided as a publicly available package posted on GitHub.