## EVENT DETAILS AND ABSTRACT

**Analysis and Probability Seminar**
**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.

**Date:** Monday, April 09, 2007

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Elton P. Hsu

**Contact email:** elton@math.northwestern.edu

**Contact Phone:** 847-491-8541

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