Phase-type Approximation of the Gerber-Shiu Function

2017/01/10 by Kazutoshi Yamazaki, Yamazaki, Kazutoshi
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G51 #60J75 #65C50 #Computational Finance (q-fin.CP) #FOS: Economics and business #Probability and Risk Models #Risk Management (q-fin.RM) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1701.02798

openalex publication_date 2017/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Sur les fonctions absolument monotones
• The Fine Structure of Asset Returns: An Empirical Investigation

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