On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options.

Donati-Martin, Catherine, Ghomrasni, Raouf, and Yor, Marc. "On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options.." Revista Matemática Iberoamericana 17.1 (2001): 179-193. <http://eudml.org/doc/39626>.

@article{Donati2001,
abstract = {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.},
author = {Donati-Martin, Catherine, Ghomrasni, Raouf, Yor, Marc},
journal = {Revista Matemática Iberoamericana},
keywords = {Movimiento browniano; Proceso de Markov; Transformada de Laplace; Ecuaciones diferenciales estocásticas; Ecuaciones funcionales; Lévy process; exponential functionals; Markov process; Brownian motion; averaged Asian option price; Laplace transform; -dimensional Markov process},
language = {eng},
number = {1},
pages = {179-193},
title = {On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options.},
url = {http://eudml.org/doc/39626},
volume = {17},
year = {2001},
}

TY - JOUR
AU - Donati-Martin, Catherine
AU - Ghomrasni, Raouf
AU - Yor, Marc
TI - On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options.
JO - Revista Matemática Iberoamericana
PY - 2001
VL - 17
IS - 1
SP - 179
EP - 193
AB - 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.
LA - eng
KW - Movimiento browniano; Proceso de Markov; Transformada de Laplace; Ecuaciones diferenciales estocásticas; Ecuaciones funcionales; Lévy process; exponential functionals; Markov process; Brownian motion; averaged Asian option price; Laplace transform; -dimensional Markov process
UR - http://eudml.org/doc/39626
ER -