Exponential functionals of spectrally one-sided l{\'e}vy processes conditioned to stay positive

Grégoire Véchambre; Grégoire Vechambre

Exponential functionals of spectrally one-sided l{\'e}vy processes conditioned to stay positive

Probability 2019-11-27 v6

Authors: Grégoire Véchambre , Grégoire Vechambre

Abstract

We study the properties of the exponential functional $\int\_0^{+ \infty} e^{- X^{\uparrow} (t)}dt$ where $X^{\uparrow}$ is a spectrally one-sided L{\'e}vy process conditioned to stay positive. In particular, we study finiteness, self-decomposability, existence of finite exponential moments, asymptotic tail at $0$ and smoothness of the density.

Keywords

exponential functional spectrally one-sided Lévy process conditioned to stay positive self-decomposability asymptotic tail smoothness of density

Cite

@article{arxiv.1507.02949,
  title  = {Exponential functionals of spectrally one-sided l{\'e}vy processes conditioned to stay positive},
  author = {Grégoire Véchambre and Grégoire Vechambre},
  journal= {arXiv preprint arXiv:1507.02949},
  year   = {2019}
}

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