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math.PR2011★ 8 cited
On the density of exponential functionals of Lévy processes
Juan Carlos Pardo, Victor Rivero, Kees van Schaik
In this paper, we study the existence of the density associated to the exponential functional of the Lévy process , \[ I_{\ee_q}:=\int_0^{\ee_q} e^{ξ_s} \, \mathrm{d}s, \] where…
math.PR2011★ 4 cited
Asymptotic Distributions of the Overshoot and Undershoots for the Lévy Insurance Risk Process in the Cramér and Convolution Equivalent Cases
Philip S Griffin, Ross A Maller, Kees van Schaik
Recent models of the insurance risk process use a Lévy process to generalise the traditional Cramér-Lundberg compound Poisson model. This paper is concerned with the behaviour of t…