Law of the exponential functional of one-sided Levy processes and Asian options

The purpose of this Note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative Levy process xi=(xi(t), t >= 0) with unbounded variation. We also derive a Geman-Yor type formula for Asian options prices in a financial market driven by e(xi). To cite this article: P Patie, C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.