First exit from an open set for a matrix-exponential Levy process

Abstract

We study the first exit from a general open set for a one-dimensional Levy process, where the Levy measure is proportional to a two-sided matrix-exponential distribution. Under appropriate conditions on the Levy measure, we obtain an explicit solution for the joint distribution of the first-exit time and the position of the Levy process upon first exit, in terms of the zeros and poles of the corresponding Laplace exponent. The present result complements several earlier works on the use of exit sets for Levy processes with algebraically similar Laplace exponents, where exits from open intervals are the main focus. Published by Elsevier B.V.