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arXiv · 1701.02798

Phase-type Approximation of the Gerber-Shiu Function

Kazutoshi Yamazaki
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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.

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Kazutoshi Yamazaki. 2017-01-10. Phase-type Approximation of the Gerber-Shiu Function. https://arxiv.org/abs/1701.02798

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