  In this paper, we consider the exponential functional
\(A_{\infty}=\int_0^\infty e^{-\xi_s}ds\) of a L{\'e}vy process \(\xi_s\) and
aim to estimate the characteristics of \(\xi_{s}\) from the distribution of
\(A_{\infty}\). We present a new approach, which allows to statistically infer
on the L{\'e}vy triplet of \(\xi_{t}\), and study the theoretical properties of
the proposed estimators. The suggested algorithms are illustrated with
numerical simulations.
