Least Squares Monte Carlo and Approximate Linear Programming: Error Bounds and Energy Real Option Application

32 Pages Posted: 25 Aug 2018

See all articles by Selvaprabu Nadarajah

Selvaprabu Nadarajah

University of Illinois at Chicago - College of Business Administration

Nicola Secomandi

Carnegie Mellon University - David A. Tepper School of Business

Date Written: August 16, 2018

Abstract

Least squares Monte Carlo (LSM) is an approximate dynamic programming (ADP) technique commonly used for the valuation of high dimensional financial and real options, but has broader applicability. It is known that the regress-later version of this method is an approximate linear programming (ALP) relaxation that implicitly provides a potential solution to a familiar ALP deficiency. Focusing on a generic finite horizon Markov decision process, we provide both theoretical and numerical backing for the usefulness of this solution, respectively using a worst-case error bound analysis and a numerical study dealing with merchant ethanol production, an energy real option application, based on an ALP heuristic that we propose. When both methodologies are applicable, our research supports the use of regress-later LSM rather than this ALP technique to approximately solve intractable Markov decision processes. Our numerical findings motivate additional research to obtain even better methods than the regress-later version of LSM.

Suggested Citation

Nadarajah, Selvaprabu and Secomandi, Nicola, Least Squares Monte Carlo and Approximate Linear Programming: Error Bounds and Energy Real Option Application (August 16, 2018). Available at SSRN: https://ssrn.com/abstract=3232687 or http://dx.doi.org/10.2139/ssrn.3232687

Selvaprabu Nadarajah (Contact Author)

University of Illinois at Chicago - College of Business Administration ( email )

601 South Morgan Street
Chicago, IL 60607
United States

Nicola Secomandi

Carnegie Mellon University - David A. Tepper School of Business ( email )

5000 Forbes Avenue
Pittsburgh, PA 15213-3890
United States

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