On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options | Zendy

Catherine Donati-Martin | Zendy; Raouf Ghomrasni | Zendy; Marc Yor | Zendy

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

Author(s) -

Catherine Donati-Martin,

Raouf Ghomrasni,

Marc Yor

Publication year - 2001

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/292

Subject(s) - statistical physics , brownian motion , exponential function , geometric brownian motion , markov chain , markov process , mathematics , mathematical economics , computer science , physics , diffusion process , mathematical analysis , statistics , knowledge management , innovation diffusion

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.

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