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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
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    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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    File URL: http://arxiv.org/pdf/1112.4351
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1112.4351.

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    Date of creation: Dec 2011
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    Handle: RePEc:arx:papers:1112.4351

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    1. N. Aleksandrov & B. Hambly, 2010. "A dual approach to multiple exercise option problems under constraints," Computational Statistics, Springer, Springer, vol. 71(3), pages 503-533, June.
    2. 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, Anderson Graduate School of Management, UCLA qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    3. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(3), pages 271-286.
    4. 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.
    5. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
    6. Denis Belomestny & Anastasia Kolodko & John Schoenmakers, 2009. "Regression methods for stochastic control problems and their convergence analysis," SFB 649 Discussion Papers SFB649DP2009-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    Cited by:
    1. Aleksandrov, Nikolay & Espinoza, Raphael & Gyurkó, Lajos, 2013. "Optimal oil production and the world supply of oil," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 37(7), pages 1248-1263.

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