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Regression methods for stochastic control problems and their convergence analysis

Author

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  • Denis Belomestny
  • Anastasia Kolodko
  • John Schoenmakers

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

  • 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.
    • Handle: RePEc:hum:wpaper:sfb649dp2009-026
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    Citations

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    Cited by:

    1. Christian Yeo, 2023. "An analysis of least squares regression and neural networks approximation for the pricing of swing options," Papers 2307.04510, arXiv.org.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

    More about this item

    Keywords

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

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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