Regression Monte Carlo for Impulse Control
MathematicS In Action, Volume 11 (2022) no. 1, pp. 73-90.

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 R is provided as a publicly available package posted on GitHub.

Published online:
DOI: 10.5802/msia.18
Classification: 93E25,  65C05,  49N25
Keywords: Impulse Control, Statistical Surrogates, Irreversible Investment
Mike Ludkovski 1

1 Department of Statistics and Applied Probability, University of California, Santa Barbara CA 93106-3110, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Mike Ludkovski. Regression Monte Carlo for Impulse Control. MathematicS In Action, Volume 11 (2022) no. 1, pp. 73-90. doi : 10.5802/msia.18. https://msia.centre-mersenne.org/articles/10.5802/msia.18/

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