Matrix representations of Wiener-Hopf factorisations for Lévy processes

The Wiener-Hopf factors of a L & eacute;vy process are the maximum and the displacement from the maximum at an independent exponential time. The majority of explicit solutions assume the upward jumps to be either phase-type or to have a rational Laplace transform, in which case the traditional expressions are lengthy expansions in terms of roots located by means of Rouch & eacute;'s theorem. As an alternative, compact matrix formulas are derived, with parameters computable by iteration schemes.