Statistical inference for exponential functionals of Lévy processes

In this paper, we consider the exponential functional $A_{\infty}=\int_0^\infty e^{-ξ_s}ds$ of a L{é}vy process $ξ_s$ and aim to estimate the characteristics of $ξ_{s}$ from the distribution of $A_{\infty}$. We present a new approach, which allows to statistically infer on the L{é}vy triplet of $ξ_{t}$, and study the theoretical properties of the proposed estimators. The suggested algorithms are illustrated with numerical simulations.

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