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

  • Lajos Gergely Gyurko
  • Ben Hambly
  • Jan Hendrik Witte
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    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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    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
    Contact details of provider: Web page: http://arxiv.org/

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    1. 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.
    2. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
    3. 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.
    4. repec:spr:compst:v:71:y:2010:i:3:p:503-533 is not listed on IDEAS
    5. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
    6. 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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