Exponential Functionals of Lévy Processes

Philippe Carmona (), Frédérique Petit () and Marc Yor ()
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Philippe Carmona: Université Paul Sabatier, Laboratoire de Statistique et Probabilités
Frédérique Petit: Université Paris VI, Laboratoire de Probabilités et Modèles Aléatoires, Casier 188
Marc Yor: Université Paris VI, Laboratoire de Probabilités et Modèles Aléatoires, Casier 188

A chapter in Lévy Processes, 2001, pp 41-55 from Springer

Abstract: Abstract The distribution of the terminal value A∞ of the exponential functional $$ {A_t}(\xi ) = \smallint _0^t{e^{{\xi _s}}}ds $$ of a Lévy process (ξ t ) t≥0 plays an important role in Mathematical Physics and Mathematical Finance. We show how this distribution can be computed by means of Lamperti’s transformation and generalized Ornstein-Uhlenbeck processes.

Keywords: Brownian Motion; Infinitesimal Generator; Compound Poisson Process; Semistable Markov Process; Asian Option (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0197-7_2

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DOI: 10.1007/978-1-4612-0197-7_2

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