  Consider the problem to explicitly calculate the law of the first passage
time T(a) of a general Levy process Z above a positive level a. In this paper
it is shown that the law of T(a) can be approximated arbitrarily closely by the
laws of T^n(a), the corresponding first passages time for X^n, where (X^n)_n is
a sequence of Levy processes whose positive jumps follow a phase-type
distribution. Subsequently, explicit expressions are derived for the laws of
T^n(a) and the upward ladder process of X^n.
  The derivation is based on an embedding of X^n into a class of Markov
additive processes and on the solution of the fundamental (matrix) Wiener-Hopf
factorisation for this class.
  This Wiener-Hopf factorisation can be computed explicitly by solving
iteratively a certain fixed point equation. It is shown that, typically, this
iteration converges geometrically fast.
