A Survey and Some Generalizations of Bessel Processes

Bessel processes play an important role in financial mathematics because of their strong relation to financial processes like geometric Brownian motion or CIR 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, i. e., CIR 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.