IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2009-026.html
   My bibliography  Save this paper

Regression methods for stochastic control problems and their convergence analysis

Author

Listed:
  • Belomestny, Denis
  • Kolodko, Anastasia
  • Schoenmakers, John G. M.

Abstract

In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particularly useful for problems with a highdimensional state space and complex dependence structure of the underlying Markov process with respect to some control. The main idea behind the algorithms is to simulate a set of trajectories under some reference measure and to use the Bellman principle combined with fast methods for approximating conditional expectations and functional optimization. Theoretical properties of the presented algorithms are investigated and the convergence to the optimal solution is proved under some assumptions. Finally, the presented methods are applied in a numerical example of a high-dimensional controlled Bermudan basket option in a financial market with a large investor.

Suggested Citation

  • 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.
  • Handle: RePEc:zbw:sfb649:sfb649dp2009-026
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/25342/1/599991771.PDF
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. 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.
    2. 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.
    3. Nicholas Andrew Yap Swee Guan, 2015. "Regression and Convex Switching System Methods for Stochastic Control Problems with Applications to Multiple-Exercise Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 26, July-Dece.
    4. Fort Gersende & Gobet Emmanuel & Moulines Eric, 2017. "MCMC design-based non-parametric regression for rare event. Application to nested risk computations," Monte Carlo Methods and Applications, De Gruyter, vol. 23(1), pages 21-42, March.
    5. Christian Yeo, 2023. "An analysis of least squares regression and neural networks approximation for the pricing of swing options," Papers 2307.04510, arXiv.org.

    More about this item

    Keywords

    Optimal stochastic control; Regression methods; Convergence analysis.;
    All these keywords.

    JEL classification:

    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

    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:zbw:sfb649:sfb649dp2009-026. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    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.