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The aim of this paper is to present the new results concerning somefunctionals of Brownian motion with drift and present their applications infinancial mathematics. We find a probabilistic representation of the Laplacetransform of special functional of geometric Brownian motion using the squaredBessel and radial Ornstein-Uhlenbeck processes. Knowing the transition densityfunctions of the above we obtain computable formulas for certain expectationsof the concerned functional. As an example we find the moments of processesrepresenting an asset price in the lognormal volatility ans Stein models.  We also present links among the geometric Brownian motion, the Markovprocesses studied by Matsumoto and Yor and the hyperbolic Bessel processes.

On some Brownian functionals and their applications to moments in lognormal and Stein stochastic volatility models