Singularities of the matrix exponent of a Markov additive process with one-sided jumps

We analyze the number of zeros of det(F(alpha)), where F(alpha) is the matrix exponent of a Markov Additive Process (MAP) with one-sided jumps. The focus is on the number of zeros in the right half of the complex plane, where F(alpha) is analytic. In addition, we also consider the case of a MAP killed at an independent exponential time. The corresponding zeros can be seen as the roots of a generalized Cramer-Lundberg equation. We argue that our results are particularly useful in fluctuation theory for MAPs, which leads to numerous applications in queueing theory and finance. (C) 2010 Elsevier B.V. All rights reserved.