Exponential functionals of Levy processes and variable annuity guaranteed benefits

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Feng, Runhuan¹  Kuznetsov, Alexey²  Yang, Fenghao² 

[1] Univ Illinois, Dept Math, Urbana, IL 61820 USA

[2] York Univ, Dept Math & Stat, N York, ON, Canada

关键词: Exponential functionals;    Levy processes;    Ornstein-Uhlenbeck process;    Mellin transform;    Meijer G-function;    Variable annuity guaranteed benefits;   

DOI  :  10.1016/j.spa.2018.03.011

来源: Elsevier

【 摘 要 】

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 Levy 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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free