Phase-type Approximation of the Gerber-Shiu Function

Abstract

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.

16 pages. Forthcoming in the Journal of the Operations Research Society of Japan, vol. 60, no. 3, 2017 (special issue of the 60th anniversary of the Operations Research Society of Japan)

References in corpus (2)

• On the optimal dividend problem for a spectrally negative Lévy process
• On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes