Fake exponential Brownian motion

On Some Exponential Functionals of Brownian Motion

In this paper, distributional questions which arise in certain Mathematical Finance models are studied: the distribution of the integral over a fixed time interval {0, T} of the exponential of Brownian motion with drift is computed explicitly, with the help of former computations made by the author for Bessel processes. The moments of this integral are obtained independently and take a particul...

Exponential functionals of Brownian motion and class one Whittaker functions

We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise al...

Exponential Functionals of Brownian Motion and Disordered Systems

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts such as continuous time finance models and one-dimensional disordered models. We study some properties of these exponential functionals in relation with the problem of a particle coupled to a heat bath in a Wiener potential. Explicit expressions for the distribution of the free energy ar...

Further Results on Exponential Functionals of Brownian Motion

On the Exponential Orlicz Norms of Stopped Brownian Motion

Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by p(x) = exp(jxjp) 1 with 0 < p 2 ) of max 0 t jBtj or jB j is finite, where B = (Bt)t 0 is standard Brownian motion and is a stopping time for B . The conditions are in terms of the moments of the stopping time . For instance, we find that max 0 t jBtj 1<1 as soon as we have: E( ) = O Ck for some constant...