TY - JOUR
T1 - Exponential functionals of Lévy processes and variable annuity guaranteed benefits
AU - Feng, Runhuan
AU - Kuznetsov, Alexey
AU - Yang, Fenghao
N1 - Funding Information:
The research of A. Kuznetsov was supported by the Natural Sciences and Engineering Research Council of Canada . The research of R. Feng is supported by the State Farm Companies Foundation.
Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/2
Y1 - 2019/2
N2 - 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.
AB - 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.
KW - Exponential functionals
KW - Lévy processes
KW - Meijer G-function
KW - Mellin transform
KW - Ornstein–Uhlenbeck process
KW - Variable annuity guaranteed benefits
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U2 - 10.1016/j.spa.2018.03.011
DO - 10.1016/j.spa.2018.03.011
M3 - Article
AN - SCOPUS:85045217154
SN - 0304-4149
VL - 129
SP - 604
EP - 625
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -