Tail asymptotics for exponential functionals of Lévy processes

Motivated by recent studies in financial mathematics and other areas, we investigate the exponential functional Z=∫0∞e-X(t)dt of a Lévy process X(t),t⩾0X(t),t⩾0. In particular, we investigate its tail asymptotics. We show that, depending on the right tail of X(1)X(1), the tail behavior of ZZ is exponential, Pareto, or extremely heavy-tailed.