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Multilevel estimation of expected exit times and other functionals of stopped diffusions

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  • Michael B. Giles
  • Francisco Bernal

Abstract

This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals which correspond to solutions to high-dimensional parabolic PDEs through the Feynman-Kac formula. In particular, it is proved that the complexity to achieve an $\varepsilon$ root-mean-square error is $O(\varepsilon^{-2}\, |\!\log \varepsilon|^3)$.

Suggested Citation

  • Michael B. Giles & Francisco Bernal, 2017. "Multilevel estimation of expected exit times and other functionals of stopped diffusions," Papers 1710.07492, arXiv.org, revised Sep 2018.
    • Handle: RePEc:arx:papers:1710.07492
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    References listed on IDEAS

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    1. K. Bujok & B. M. Hambly & C. Reisinger, 2015. "Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 579-604, September.
    2. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    3. Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
    4. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
    5. Sam Howison, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 2: Bermudan Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 91-104.
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