Estimating the Gerber-Shiu Function in Lévy Insurance Risk Model by Fourier-Cosine Series Expansion

Wen Su and Yunyun Wang
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Wen Su: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Yunyun Wang: Department of Econometrics and Business Statistics, School of Business, Monash University, Melbourne 3800, Australia

Mathematics, 2021, vol. 9, issue 12, 1-18

Abstract: In this paper, we propose an estimator for the Gerber–Shiu function in a pure-jump Lévy risk model when the surplus process is observed at a high frequency. The estimator is constructed based on the Fourier–Cosine series expansion and its consistency property is thoroughly studied. Simulation examples reveal that our estimator performs better than the Fourier transform method estimator when the sample size is finite.

Keywords: Gerber–Shiu function; Lévy insurance risk model; Fourier–Cosine series expansion; estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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