Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Runhuan Feng; Alexey Kuznetsov; Fenghao Yang

doi:10.1016/j.spa.2018.03.011

Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Runhuan Feng, Alexey Kuznetsov, Fenghao Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	604-625
Number of pages	22
Journal	Stochastic Processes and their Applications
Volume	129
Issue number	2
DOIs	https://doi.org/10.1016/j.spa.2018.03.011
State	Published - Feb 2019

Keywords

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

Online availability

10.1016/j.spa.2018.03.011

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title = "Exponential functionals of L{\'e}vy processes and variable annuity guaranteed benefits",

abstract = "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 L{\'e}vy 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.",

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author = "Runhuan Feng and Alexey Kuznetsov and Fenghao Yang",

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T1 - Exponential functionals of Lévy processes and variable annuity guaranteed benefits

AU - Feng, Runhuan

AU - Kuznetsov, Alexey

AU - Yang, Fenghao

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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Exponential functionals of Lévy processes and variable annuity guaranteed benefits

Abstract

Keywords

ASJC Scopus subject areas

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