Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

- C. DONATI-MARTIN
- R. GHOMRASNI
**M. YOR**

**Code(s) de Classification MSC:**

- 60J65 Brownian motion, See also {58G32}
- 60J30 Processes with independent increments

**Résumé:** 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.

**Mots Clés:** *exponentials of Brownian motion; Asian options; generalized Ornstein-Uhlenbeck processes*

**Date:** 1999-03-26

**Prépublication numéro:** *PMA-495*