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Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes

Martin, R. J., Kearney, M. J. and Craster, R. V. (2019) Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes Journal of Physics A: Mathematical and Theoretical, 52 (13). pp. 1-33.

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Abstract

The first-passage problem of the Ornstein-Uhlenbeck (OU) process to a boundary is a long-standing problem with no known closed-form solution except in specifc cases. Taking this as a starting-point, and extending to a general mean-reverting process, we investigate the long- and short-time asymptotics using a combination of Hopf-Cole and Laplace transform techniques. As a result we are able to give a single formula that is correct in both limits, as well as being exact in certain special cases. We demonstrate the results using a variety of other models.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences
Authors :
NameEmailORCID
Martin, R. J.
Kearney, M. J.M.J.Kearney@surrey.ac.uk
Craster, R. V.
Date : 7 March 2019
DOI : 10.1088/1751-8121/ab0836/meta
Copyright Disclaimer : © 2019 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/ab0836/meta
Depositing User : Christine Daoutis
Date Deposited : 01 Mar 2019 12:58
Last Modified : 08 Mar 2020 02:08
URI: http://epubs.surrey.ac.uk/id/eprint/850598

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