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 Lévy process with unbounded variation. We also derive a Geman–Yor type formula for Asian options prices in a financial market driven by .
L'object de cette Note est de donner une représentation, en terme d'une série entière, de la distribution de la fonctionnelle exponentielle, considérée en un temps exponentiel indépendant, d'un processus de Lévy ξ spectralement négatif, à variation infinie et pouvant être tué. Nous en déduisons une formule du type Geman–Yor pour le prix des options asiatiques dans un marché financier dirigé par .
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Pierre Patie 1
@article{CRMATH_2009__347_7-8_407_0, author = {Pierre Patie}, title = {Law of the exponential functional of one-sided {L\'evy} processes and {Asian} options}, journal = {Comptes Rendus. Math\'ematique}, pages = {407--411}, publisher = {Elsevier}, volume = {347}, number = {7-8}, year = {2009}, doi = {10.1016/j.crma.2009.02.013}, language = {en}, }
Pierre Patie. Law of the exponential functional of one-sided Lévy processes and Asian options. Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 407-411. doi : 10.1016/j.crma.2009.02.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.02.013/
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