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We determine the rate of decrease of the right tail distribution of theexponential functional of a Levy process with a convolution equivalent Levymeasure. Our main result establishes that it decreases as the right tail of theimage under the exponential function of the Levy measure of the underlying Levyprocess. The method of proof relies on fluctuation theory of Levy processes andan explicit path-wise representation of the exponential functional as theexponential functional of a bivariate subordinator. Our techniques allow us toestablish rather general estimates of the measure of the excursions out fromzero for the underlying Levy process reflected in its past infimum, whose areaunder the exponential of the excursion path exceed a given value.

Tail asymptotics for exponential functionals of Levy processes: the convolution equivalent case