  The Gerber-Shiu function provides a way of measuring the risk of an insurance
company. It is given by the expected value of a function that depends on the
ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation
requires the evaluation of the overshoot/undershoot distributions of the
surplus process at ruin. In this paper, we use the recent developments of the
fluctuation theory and approximate it in a closed form by fitting the
underlying process by phase-type Levy processes. A sequence of numerical
results are given.
