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Estimating Gerber-Shiu functions from discretely observed Lévy driven surplus. (English) Zbl 1394.62147

Summary: 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 \(L^2\)-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.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
60G51 Processes with independent increments; Lévy processes
62M05 Markov processes: estimation; hidden Markov models
62G20 Asymptotic properties of nonparametric inference
91B30 Risk theory, insurance (MSC2010)
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