A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the size of the local hypercubes involved in the regressions, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants. This model takes into account electricity demand, cointegrated fuel prices, carbon price and random outages of power plants. It computes the optimal level of investment in each generation technology, considered as a whole, w.r.t. the electricity spot price. This electricity price is itself built according to a new extended structural model. In particular, it is a function of several factors, among which the installed capacities. The evolution of the optimal generation mix is illustrated on a realistic numerical problem in dimension eight, i.e. with two different technologies and six random factors.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hobbs, Benjamin F., 1995. "Optimization methods for electric utility resource planning," European Journal of Operational Research, Elsevier, vol. 83(1), pages 1-20, May.
- Walter Schachermayer & Josef Teichmann, 2007. "How close are the option pricing formulas of Bachelier and Black-Merton-Scholes?," Papers 0711.1272, arXiv.org.
- Kerry Back & Dirk Paulsen, 2009. "Open-Loop Equilibria and Perfect Competition in Option Exercise Games," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4531-4552, November.
- Foley, A.M. & Ó Gallachóir, B.P. & Hur, J. & Baldick, R. & McKeogh, E.J., 2010. "A strategic review of electricity systems models," Energy, Elsevier, vol. 35(12), pages 4522-4530.
- René Aïd & Luciano Campi & Adrien Nguyen Huu & Nizar Touzi, 2009. "A Structural Risk-Neutral Model Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 925-947.
- Connolly, D. & Lund, H. & Mathiesen, B.V. & Leahy, M., 2010. "A review of computer tools for analysing the integration of renewable energy into various energy systems," Applied Energy, Elsevier, vol. 87(4), pages 1059-1082, April.
- Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
- Bar-Ilan, Avner & Sulem, Agnes & Zanello, Alessandro, 2002. "Time-to-build and capacity choice," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 69-98, January.
- René Aid & Luciano Campi & Adrien Nguyen Huu & Nizar Touzi, 2009. "A structural risk-neutral model of electricity prices," Post-Print hal-00390690, HAL.
- Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
- Dyner, Isaac & Larsen, Erik R., 2001. "From planning to strategy in the electricity industry," Energy Policy, Elsevier, vol. 29(13), pages 1145-1154, November.
- Almut E. D. Veraart & Luitgard A. M. Veraart, 2009.
"Stochastic volatility and stochastic leverage,"
CREATES Research Papers
2009-20, Department of Economics and Business Economics, Aarhus University.
- 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.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1210.8175. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.