Estimating Gerber–Shiu functions from discretely observed Lévy driven surplus

Yasutaka Shimizu and Zhimin Zhang

Insurance: Mathematics and Economics, 2017, vol. 74, issue C, 84-98

Abstract: Consider an insurance surplus process driven by a Lévy subordinator, which is observed at discrete time points. An estimator of the Gerber–Shiu function is proposed via the empirical Fourier transform of the Gerber–Shiu function. By evaluating its mean squared error, we show the L2-consistency of the estimator under the assumption of high-frequency observation of the surplus process in a long term. Simulation studies are also presented to show the finite sample performance of the proposed estimator.

Keywords: Lévy risk model; Gerber–Shiu function; Fourier inversion; L2-consistency; Estimation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:74:y:2017:i:c:p:84-98

DOI: 10.1016/j.insmatheco.2017.02.006

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