Abstract
A non-parametric estimator of the Gerber–Shiu function is proposed for a risk process with a compound Poisson claim process plus a diffusion perturbation; the Wiener–Poisson risk model. The estimator is based on a regularized inversion of an empirical-type estimator of the Laplace transform of the Gerber–Shiu function. We show the weak consistency of the estimator in the sense of an integrated squared error with the rate of convergence.
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