C. Donati-martin et al., On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options, REV MAT IBE, 17(1), 2001, pp. 179-193
We obtain a closed formula for the Laplace transform of the first moment of
certain exponential functionals of Brownian motion with drift, which gives
the price of Asian options. The proof relies on an identity in law between
the average on [0, t] of a geometric Brownian motion and the value at time
t of a Markov process, for which we can compute explicitly the resolvent.