Bernoulli

  • Bernoulli
  • Volume 9, Number 2 (2003), 313-349.

A survey and some generalizations of Bessel processes

Anja Göing-Jaeschke and Marc Yor

Full-text: Open access

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.

Article information

Source
Bernoulli, Volume 9, Number 2 (2003), 313-349.

Dates
First available in Project Euclid: 6 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.bj/1068128980

Digital Object Identifier
doi:10.3150/bj/1068128980

Mathematical Reviews number (MathSciNet)
MR1997032

Zentralblatt MATH identifier
1038.60079

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

Citation

Göing-Jaeschke, Anja; Yor, Marc. A survey and some generalizations of Bessel processes. Bernoulli 9 (2003), no. 2, 313--349. doi:10.3150/bj/1068128980. https://projecteuclid.org/euclid.bj/1068128980


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