IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1605.07500.html
   My bibliography  Save this paper

Pathwise Iteration for Backward SDEs

Author

Listed:
  • Christian Bender
  • Christian Gaertner
  • Nikolaus Schweizer

Abstract

We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., iterated integrals of previous approximations. Our approach allows us to compute and iteratively improve upper and lower bounds on the true solution starting from an arbitrary and possibly crude input approximation. We demonstrate the benefits of our approach in a high dimensional financial application.

Suggested Citation

  • Christian Bender & Christian Gaertner & Nikolaus Schweizer, 2016. "Pathwise Iteration for Backward SDEs," Papers 1605.07500, arXiv.org, revised Jun 2016.
  • Handle: RePEc:arx:papers:1605.07500
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1605.07500
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nan Chen & Paul Glasserman, 2007. "Additive and multiplicative duals for American option pricing," Finance and Stochastics, Springer, vol. 11(2), pages 153-179, April.
    2. Jean-Paul Laurent & Philippe Amzelek & Joe Bonnaud, 2014. "An overview of the valuation of collateralized derivative contracts," Post-Print hal-03679423, HAL.
    3. 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.
    4. repec:dau:papers:123456789/5524 is not listed on IDEAS
    5. David B. Brown & James E. Smith & Peng Sun, 2010. "Information Relaxations and Duality in Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 785-801, August.
    6. Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, vol. 10(1), pages 27-49, January.
    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.
    8. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    10. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    11. Bergman, Yaacov Z, 1995. "Option Pricing with Differential Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 475-500.
    12. Jean-Paul Laurent & Philippe Amzelek & Joe Bonnaud, 2014. "An overview of the valuation of collateralized derivative contracts," Review of Derivatives Research, Springer, vol. 17(3), pages 261-286, October.
    13. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    14. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    Full references (including those not matched with items on IDEAS)

    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. Helin Zhu & Fan Ye & Enlu Zhou, 2015. "Fast estimation of true bounds on Bermudan option prices under jump-diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1885-1900, November.
    2. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.
    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. Dragos Florin Ciocan & Velibor V. Mišić, 2022. "Interpretable Optimal Stopping," Management Science, INFORMS, vol. 68(3), pages 1616-1638, March.
    6. Denis Belomestny & John Schoenmakers, 2021. "From optimal martingales to randomized dual optimal stopping," Papers 2102.01533, arXiv.org.
    7. Denis Belomestny & Christian Bender & John Schoenmakers, 2009. "True Upper Bounds For Bermudan Products Via Non‐Nested Monte Carlo," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 53-71, January.
    8. John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
    9. 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.
    10. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    11. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    12. Mark Broadie & Weiwei Shen, 2016. "High-Dimensional Portfolio Optimization With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-49, June.
    13. Louis Bhim & Reiichiro Kawai, 2018. "Smooth Upper Bounds For The Price Function Of American Style Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-38, February.
    14. Ivan Guo & Nicolas Langren'e & Jiahao Wu, 2023. "Simultaneous upper and lower bounds of American option prices with hedging via neural networks," Papers 2302.12439, arXiv.org.
    15. Bradley Sturt, 2021. "A nonparametric algorithm for optimal stopping based on robust optimization," Papers 2103.03300, arXiv.org, revised Mar 2023.
    16. Wei, Wei & Zhu, Dan, 2022. "Generic improvements to least squares monte carlo methods with applications to optimal stopping problems," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1132-1144.
    17. David B. Brown & Martin B. Haugh, 2017. "Information Relaxation Bounds for Infinite Horizon Markov Decision Processes," Operations Research, INFORMS, vol. 65(5), pages 1355-1379, October.
    18. Mark S. Joshi, 2016. "Analysing the bias in the primal-dual upper bound method for early exercisable derivatives: bounds, estimation and removal," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 519-533, April.
    19. Alessio Trivella & Danial Mohseni-Taheri & Selvaprabu Nadarajah, 2023. "Meeting Corporate Renewable Power Targets," Management Science, INFORMS, vol. 69(1), pages 491-512, January.
    20. 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.

    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:1605.07500. 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.