Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Runhuan Feng, Alexey Kuznetsov, Fenghao Yang

Research output: Contribution to journalArticlepeer-review


Exponential functionals of Brownian motion have been extensively studied in financial and insurance mathematics due to their broad applications, for example, in the pricing of Asian options. The Black–Scholes model is appealing because of mathematical tractability, yet empirical evidence shows that geometric Brownian motion does not adequately capture features of market equity returns. One popular alternative for modeling equity returns consists in replacing the geometric Brownian motion by an exponential of a Lévy process. In this paper we use this latter model to study variable annuity guaranteed benefits and to compute explicitly the distribution of certain exponential functionals.

Original languageEnglish (US)
Pages (from-to)604-625
Number of pages22
JournalStochastic Processes and their Applications
Issue number2
StatePublished - Feb 2019


  • Exponential functionals
  • Lévy processes
  • Meijer G-function
  • Mellin transform
  • Ornstein–Uhlenbeck process
  • Variable annuity guaranteed benefits

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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