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arXiv · 1810.13010

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

R. J. Martin·M. J. Kearney·R. V. Craster
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Abstract

The first-passage problem of the Ornstein-Uhlenbeck process to a boundary is a long-standing problem with no known closed-form solution except in specific 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.

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R. J. Martin, M. J. Kearney, R. V. Craster. 2018-10-30. Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes. https://doi.org/10.1088/1751-8121/ab0836

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