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 ) d t of a Lévy process X ( t ) , t ⩾ 0 . In particular, we investigate its tail asymptotics. We show that, depending on the right tail of X ( 1 ) , the tail behavior of Z is exponential, Pareto, or extremely heavy-tailed.