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Monte Carlo methods via a dual approach for some discrete time stochastic control problems

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  • Lajos Gergely Gyurko
  • Ben Hambly
  • Jan Hendrik Witte

Abstract

We consider a class of discrete time stochastic control problems motivated by some financial applications. We use a pathwise stochastic control approach to provide a dual formulation of the problem. This enables us to develop a numerical technique for obtaining an estimate of the value function which improves on purely regression based methods. We demonstrate the competitiveness of the method on the example of a gas storage valuation problem.

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  • Lajos Gergely Gyurko & Ben Hambly & Jan Hendrik Witte, 2011. "Monte Carlo methods via a dual approach for some discrete time stochastic control problems," Papers 1112.4351, arXiv.org.
    • Handle: RePEc:arx:papers:1112.4351
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    References listed on IDEAS

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    1. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
    2. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    3. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    4. Rene Carmona & Michael Ludkovski, 2010. "Valuation of energy storage: an optimal switching approach," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 359-374.
    5. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    6. Belomestny, Denis & Kolodko, Anastasia & Schoenmakers, John G. M., 2009. "Regression methods for stochastic control problems and their convergence analysis," SFB 649 Discussion Papers 2009-026, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. 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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    Cited by:

    1. Mr. Nikolay Aleksandrov & Mr. lajos Gyurko & Mr. Raphael A Espinoza, 2012. "Optimal Oil Production and the World Supply of Oil," IMF Working Papers 2012/294, International Monetary Fund.
    2. Aleksandrov, Nikolay & Espinoza, Raphael & Gyurkó, Lajos, 2013. "Optimal oil production and the world supply of oil," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1248-1263.

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