The distribution of the maximum of a Lévy processes with positive jumps of phase-type

Author: Ernesto Mordecki.

Posted: 22/10/2002 (Final version). Status: Submitted

Abstract: Consider a Lévy process with finite intensity positive jumps of the phase-type and arbitrary negative jumps. Assume that the process either is killed at a constant rate or drifts to minus infinity. We show that the distribution of the overall maximum of this process is also of phase-type, and find the distribution of this random variable. Previous results (hyperexpontial positive jumps) are obtained as a particular case.

Keywords: Lévy process, Phase-type distributions, maximum of a Lévy process, hyperexponential distributions, ruin probabilities.

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[Articles by Ernesto Mordecki]