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Nonparametric estimation of the expected discounted penalty function in the compound Poisson model. (English) Zbl 1493.62165

Summary: We propose a nonparametric estimator of the expected discounted penalty function in the compound Poisson risk model. We use a projection estimator on the Laguerre basis and we compute the coefficients using Plancherel theorem. We provide an upper bound on the MISE of our estimator, and we show it achieves parametric rates of convergence on Sobolev-Laguerre spaces without needing a bias-variance compromise. Moreover, we compare our estimator with the Laguerre deconvolution method. We compute an upper bound of the MISE of the Laguerre deconvolution estimator and we compare it on Sobolev-Laguerre spaces with our estimator. Finally, we compare these estimators on simulated data.

MSC:

62G05 Nonparametric estimation
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G70 Statistical methods; risk measures
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