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Simulation Methods for Stochastic Storage Problems: A Statistical Learning Perspective

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  • Michael Ludkovski
  • Aditya Maheshwari

Abstract

We consider solution of stochastic storage problems through regression Monte Carlo (RMC) methods. Taking a statistical learning perspective, we develop the dynamic emulation algorithm (DEA) that unifies the different existing approaches in a single modular template. We then investigate the two central aspects of regression architecture and experimental design that constitute DEA. For the regression piece, we discuss various non-parametric approaches, in particular introducing the use of Gaussian process regression in the context of stochastic storage. For simulation design, we compare the performance of traditional design (grid discretization), against space-filling, and several adaptive alternatives. The overall DEA template is illustrated with multiple examples drawing from natural gas storage valuation and optimal control of back-up generator in a microgrid.

Suggested Citation

  • Michael Ludkovski & Aditya Maheshwari, 2018. "Simulation Methods for Stochastic Storage Problems: A Statistical Learning Perspective," Papers 1803.11309, arXiv.org.
    • Handle: RePEc:arx:papers:1803.11309
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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.
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    8. Nadarajah, Selvaprabu & Margot, François & Secomandi, Nicola, 2017. "Comparison of least squares Monte Carlo methods with applications to energy real options," European Journal of Operational Research, Elsevier, vol. 256(1), pages 196-204.
    9. Rene Carmona & Michael Ludkovski, 2010. "Valuation of energy storage: an optimal switching approach," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 359-374.
    10. Jain, Shashi & Oosterlee, Cornelis W., 2015. "The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 412-431.
    11. 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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