EVENT DETAILS AND ABSTRACT

Title: On infima of Levy processes and application in risk theory
Speaker: Professor Zoran Vondracek
Speaker Info: University of Zagreb
Brief Description:
Special Note:
Abstract:

Let $Y$ be a one-dimensional L\'evy process, $C$ an independent subordinator and $X=Y-C$. We discuss the infimum process of $X$. To be more specific, we are interested in times when a new infimum is reached by a jump of the subordinator $C$. We give a necessary and sufficient condition that such times are discrete. A motivation for this problem comes from the ruin theory where $X$ can be interpreted as a perturbed risk process. In case $Y$ is >> spectrally negative, decomposition of $X$ at times when a new infimum is reached by a jump of a subordinator leads to a Pollaczek-Hintchin-type formula for the probability of ruin.