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Regression Monte Carlo for Impulse Control

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  • Mike Ludkovski

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.

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  • Mike Ludkovski, 2022. "Regression Monte Carlo for Impulse Control," Papers 2203.06539, arXiv.org.
    • Handle: RePEc:arx:papers:2203.06539
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Christensen, Sören, 2014. "On the solution of general impulse control problems using superharmonic functions," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 709-729.
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    8. Matteo Basei, 2018. "Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates," Papers 1803.08166, arXiv.org, revised Mar 2019.
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    13. Mike Ludkovski, 2020. "mlOSP: Towards a Unified Implementation of Regression Monte Carlo Algorithms," Papers 2012.00729, arXiv.org, revised Oct 2022.
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    18. repec:dau:papers:123456789/14292 is not listed on IDEAS
    19. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Full references (including those not matched with items on IDEAS)

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