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,] of a geometric Brownian motion and the value at time of a Markov process for which we can compute explicitly the resolvent.
Cite this article
Catherine Donati-Martin, Raouf Ghomrasni, Marc Yor, On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options. Rev. Mat. Iberoam. 17 (2001), no. 1, pp. 179–193DOI 10.4171/RMI/292