Regression Monte Carlo for Impulse Control

TL;DR

This paper introduces a Regression Monte Carlo algorithm for stochastic impulse control problems, using statistical surrogates to approximate continuation and intervention functions, demonstrated through case studies and implemented in R.

Contribution

It presents a novel numerical method combining regression and Monte Carlo techniques for impulse control, with practical implementation and case studies.

Findings

Effective approximation of continuation functions

Flexible and extensible numerical scheme

Open-source R implementation

Abstract

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.