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

Catherine Donati-Martin; Raouf Ghomrasni; Marc Yor

Revista Matemática Iberoamericana (2001)

- Volume: 17, Issue: 1, page 179-193
- ISSN: 0213-2230

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topDonati-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 -

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