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On the rates of convergence of simulation based optimization algorithms for optimal stopping problems

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  • Denis Belomestny

Abstract

In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large deviation theory for the increments of empirical processes, we derive optimal convergence rates and show that they can not be improved in general. The rates derived provide a guide to the choice of the number of simulated paths needed in optimization step, which is crucial for the good performance of any simulation based optimization algorithm. Finally, we present a numerical example of solving optimal stopping problem arising in option pricing that illustrates our theoretical findings.

Suggested Citation

  • Denis Belomestny, 2009. "On the rates of convergence of simulation based optimization algorithms for optimal stopping problems," Papers 0909.3570, arXiv.org.
    • Handle: RePEc:arx:papers:0909.3570
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    File URL: http://arxiv.org/pdf/0909.3570
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    Cited by:

    1. David A. Goldberg & Yilun Chen, 2018. "Beating the curse of dimensionality in options pricing and optimal stopping," Papers 1807.02227, arXiv.org, revised Aug 2018.
    2. Christian Bayer & Ra'ul Tempone & Soren Wolfers, 2018. "Pricing American Options by Exercise Rate Optimization," Papers 1809.07300, arXiv.org, revised Aug 2019.

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