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 metho...

Abstract We investigate the effect of estimation error on backtests expected shortfall (ES) forecasts. These are based first-order conditions a recently introduced family jointly consistent loss functions for value-at-risk (VaR) and ES. For both single multiperiod horizons, we provide explicit expressions additional terms in asymptotic covariance matrix that result from error, propose robust te...