IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1112.4351.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1112.4351
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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, vol. 37(7), pages 1248-1263.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Secomandi, Nicola & Seppi, Duane J., 2014. "Real Options and Merchant Operations of Energy and Other Commodities," Foundations and Trends(R) in Technology, Information and Operations Management, now publishers, vol. 6(3-4), pages 161-331, July.
    2. Denis Belomestny & Grigori Milstein & Vladimir Spokoiny, 2009. "Regression methods in pricing American and Bermudan options using consumption processes," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 315-327.
    3. Helin Zhu & Fan Ye & Enlu Zhou, 2013. "Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes," Papers 1305.4321, arXiv.org.
    4. Vijay V. Desai & Vivek F. Farias & Ciamac C. Moallemi, 2012. "Pathwise Optimization for Optimal Stopping Problems," Management Science, INFORMS, vol. 58(12), pages 2292-2308, December.
    5. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2008. "Simulation-based pricing of convertible bonds," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 310-331, March.
    6. Jérôme Lelong, 2019. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Working Papers hal-01983115, HAL.
    7. Bradley Sturt, 2021. "A nonparametric algorithm for optimal stopping based on robust optimization," Papers 2103.03300, arXiv.org, revised Mar 2023.
    8. Lukas Gonon, 2022. "Deep neural network expressivity for optimal stopping problems," Papers 2210.10443, arXiv.org.
    9. Burcu Aydoğan & Ümit Aksoy & Ömür Uğur, 2018. "On the methods of pricing American options: case study," Annals of Operations Research, Springer, vol. 260(1), pages 79-94, January.
    10. Mark Joshi & Oh Kang Kwon, 2016. "Least Squares Monte Carlo Credit Value Adjustment With Small And Unidirectional Bias," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-16, December.
    11. Nan Chen & Yanchu Liu, 2014. "American Option Sensitivities Estimation via a Generalized Infinitesimal Perturbation Analysis Approach," Operations Research, INFORMS, vol. 62(3), pages 616-632, June.
    12. Cerrato, Mario & Abbasyan, Abdollah, 2008. "Optimal Martingales and American Option Pricing," SIRE Discussion Papers 2008-36, Scottish Institute for Research in Economics (SIRE).
    13. J'er^ome Lelong, 2019. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Papers 1901.05672, arXiv.org, revised Jul 2020.
    14. Chen Liu & Henry Schellhorn & Qidi Peng, 2019. "American Option Pricing With Regression: Convergence Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-31, December.
    15. Roberto Baviera & Lorenzo Giada, 2013. "A perturbative approach to Bermudan options pricing with applications," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 255-263, January.
    16. Maximilian Mair & Jan Maruhn, 2013. "On the primal-dual algorithm for callable Bermudan options," Review of Derivatives Research, Springer, vol. 16(1), pages 79-110, April.
    17. Nicolas Essis-Breton & Patrice Gaillardetz, 2020. "Fast Lower and Upper Estimates for the Price of Constrained Multiple Exercise American Options by Single Pass Lookahead Search and Nearest-Neighbor Martingale," Papers 2002.11258, arXiv.org.
    18. John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
    19. Jin, Xing & Yang, Cheng-Yu, 2016. "Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 65-77.
    20. John Schoenmakers & Junbo Huang & Jianing Zhang, 2011. "Optimal dual martingales, their analysis and application to new algorithms for Bermudan products," Papers 1111.6038, arXiv.org, revised Feb 2012.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1112.4351. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.