Statistical inference for exponential functionals of Lévy processes

Abstract: 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.