  In this work, we consider moments of exponential functionals of L\'{e}vy
processes on a deterministic horizon. We derive two convolutional identities
regarding these moments. The first one relates the complex moments of the
exponential functional of a general L\'{e}vy process up to a deterministic time
to those of the dual L\'{e}vy process. The second convolutional identity links
the complex moments of the exponential functional of a L\'{e}vy process, which
is not a compound Poisson process, to those of the exponential functionals of
its ascending/descending ladder heights on a random horizon determined by the
respective local times. As a consequence, we derive a universal expression for
the half-negative moment of the exponential functional of any symmetric
L\'{e}vy process, which resembles in its universality the passage time of
symmetric random walks. The $(n-1/2)^{th}$, $n\geq 0$ moments are also
discussed. On the other hand, under extremely mild conditions, we obtain a
series expansion for the complex moments (including those with negative real
part) of the exponential functionals of subordinators. This significantly
extends previous results and offers neat expressions for the negative real
moments. In a special case, it turns out that the Riemann zeta function is the
minus first moment of the exponential functional of the Gamma subordinator
indexed in time.
