Computing mean first exit times for stochastic processes using multi-level Monte Carlo

Desmond Higham; Mikolaj Roj; C. Laroque; J. Himmelspach; R. Pasupathy; O. Rose; A.M. Uhrmacher

doi:10.1109/WSC.2012.6465219

Computing mean first exit times for stochastic processes using multi-level Monte Carlo

Desmond Higham, Mikolaj Roj, C. Laroque (Editor), J. Himmelspach (Editor), R. Pasupathy (Editor), O. Rose (Editor), A.M. Uhrmacher

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The multi-level approach developed by Giles (2008) can be used to estimate mean first exit times for stochastic differential equations, which are of interest in finance, physics and chemical kinetics. Multi-level improves the computational expense of standard Monte Carlo in this setting by an order of magnitude. More precisely, for a target accuracy of TOL, so that the root mean square error of the estimator is O(TOL), the O(TOL-4) cost of standard Monte Carlo can be reduced to O(TOL-3|log(TOL)|1/2) with a multi-level scheme. This result was established in Higham, Mao, Roj, Song, and Yin (2013), and illustrated on some scalar examples. Here, we briefly overview the algorithm and present some new computational results in higher dimensions.

Original language	English
Title of host publication	Proceedings of the 2012 Winter Simulation Conference (WSC)
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
ISBN (Print)	978-1-4673-4779-2
DOIs	https://doi.org/10.1109/WSC.2012.6465219
Publication status	Published - 2012

Keywords

complexity theory
networking
multi-level Monte Carlo method
computational efficiency

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10.1109/WSC.2012.6465219

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Higham, D., Roj, M., Laroque, C. (Ed.), Himmelspach, J. (Ed.), Pasupathy, R. (Ed.), Rose, O. (Ed.), & Uhrmacher, A. M. (2012). Computing mean first exit times for stochastic processes using multi-level Monte Carlo. In Proceedings of the 2012 Winter Simulation Conference (WSC) Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/WSC.2012.6465219

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abstract = "The multi-level approach developed by Giles (2008) can be used to estimate mean first exit times for stochastic differential equations, which are of interest in finance, physics and chemical kinetics. Multi-level improves the computational expense of standard Monte Carlo in this setting by an order of magnitude. More precisely, for a target accuracy of TOL, so that the root mean square error of the estimator is O(TOL), the O(TOL-4) cost of standard Monte Carlo can be reduced to O(TOL-3|log(TOL)|1/2) with a multi-level scheme. This result was established in Higham, Mao, Roj, Song, and Yin (2013), and illustrated on some scalar examples. Here, we briefly overview the algorithm and present some new computational results in higher dimensions.",

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A2 - Himmelspach, J.

A2 - Pasupathy, R.

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N2 - The multi-level approach developed by Giles (2008) can be used to estimate mean first exit times for stochastic differential equations, which are of interest in finance, physics and chemical kinetics. Multi-level improves the computational expense of standard Monte Carlo in this setting by an order of magnitude. More precisely, for a target accuracy of TOL, so that the root mean square error of the estimator is O(TOL), the O(TOL-4) cost of standard Monte Carlo can be reduced to O(TOL-3|log(TOL)|1/2) with a multi-level scheme. This result was established in Higham, Mao, Roj, Song, and Yin (2013), and illustrated on some scalar examples. Here, we briefly overview the algorithm and present some new computational results in higher dimensions.

AB - The multi-level approach developed by Giles (2008) can be used to estimate mean first exit times for stochastic differential equations, which are of interest in finance, physics and chemical kinetics. Multi-level improves the computational expense of standard Monte Carlo in this setting by an order of magnitude. More precisely, for a target accuracy of TOL, so that the root mean square error of the estimator is O(TOL), the O(TOL-4) cost of standard Monte Carlo can be reduced to O(TOL-3|log(TOL)|1/2) with a multi-level scheme. This result was established in Higham, Mao, Roj, Song, and Yin (2013), and illustrated on some scalar examples. Here, we briefly overview the algorithm and present some new computational results in higher dimensions.

KW - complexity theory

KW - networking

KW - multi-level Monte Carlo method

KW - computational efficiency

U2 - 10.1109/WSC.2012.6465219

DO - 10.1109/WSC.2012.6465219

M3 - Conference contribution

SN - 978-1-4673-4779-2

BT - Proceedings of the 2012 Winter Simulation Conference (WSC)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -

Computing mean first exit times for stochastic processes using multi-level Monte Carlo

Abstract

Keywords

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