Nonparametric estimation of the expected discounted penalty function in the compound Poisson model

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