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April 2003 A survey and some generalizations of Bessel processes
Anja Göing-Jaeschke, Marc Yor
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Bernoulli 9(2): 313-349 (April 2003). DOI: 10.3150/bj/1068128980

Abstract

Bessel processes play an important role in financial mathematics because of their strong relation to financial models such as geometric Brownian motion or Cox-Ingersoll-Ross processes. We are interested in the first time Bessel processes and, more generally, radial Ornstein-Uhlenbeck processes hit a given barrier. We give explicit expressions of the Laplace transforms of first hitting times by (squared) radial Ornstein-Uhlenbeck processes, that is, Cox-Ingersoll-Ross processes. As a natural extension we study squared Bessel processes and squared Ornstein-Uhlenbeck processes with negative dimensions or negative starting points and derive their properties.

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Anja Göing-Jaeschke. Marc Yor. "A survey and some generalizations of Bessel processes." Bernoulli 9 (2) 313 - 349, April 2003. https://doi.org/10.3150/bj/1068128980

Information

Published: April 2003
First available in Project Euclid: 6 November 2003

zbMATH: 1038.60079
MathSciNet: MR1997032
Digital Object Identifier: 10.3150/bj/1068128980

Keywords: Bessel processes with negative dimension , Cox-Ingersoll-Ross Ornstein-Uhlenbeck processes , first hitting times

Rights: Copyright © 2003 Bernoulli Society for Mathematical Statistics and Probability

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Vol.9 • No. 2 • April 2003
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