Statistical inference for exponential functionals of Lévy processes

Abstract

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.

28 pages, 5 figures

References in corpus (4)

• Statistical inference for time-changed Lévy processes via composite characteristic function estimation
• On the distribution of exponential functionals for Levy processes with jumps of rational transform
• Distributional properties of exponential functionals of Levy processes
• On the minimal travel time needed to collect n items on a circle