Exponential Functionals of Lévy Processes

  • Philippe Carmona
  • Frédérique Petit
  • Marc Yor

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

Filtration Rosen Volatility sinO 

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Philippe Carmona
    • 1
  • Frédérique Petit
    • 2
  • Marc Yor
    • 2
  1. 1.Laboratoire de Statistique et ProbabilitésUniversité Paul SabatierToulouse Cedex 04France
  2. 2.Laboratoire de Probabilités et Modèles Aléatoires, Casier 188Université Paris VIParisFrance

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