  The aim of this paper is to present the new results concerning some
functionals of Brownian motion with drift and present their applications in
financial mathematics. We find a probabilistic representation of the Laplace
transform of special functional of geometric Brownian motion using the squared
Bessel and radial Ornstein-Uhlenbeck processes. Knowing the transition density
functions of the above we obtain computable formulas for certain expectations
of the concerned functional. As an example we find the moments of processes
representing an asset price in the lognormal volatility ans Stein models.
  We also present links among the geometric Brownian motion, the Markov
processes studied by Matsumoto and Yor and the hyperbolic Bessel processes.
