Estimating Gerber-Shiu functions from discretely observed Lévy driven surplus

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.