This paper examines the problem of accurately estimating the expected value and variance of the aggregate claims for each policyholder. To this end, the framework of generalized linear models (GLMs) for aggregate claims is extended to a structure of frequentist generalized additive models (GAMs) based on cubic penalized regression splines. The new structure could allow more flexible nonlinear and/or nonparametric trend terms for the marginal claim frequency and conditional claim severity models. This nonparametric approach is illustrated through simulation. The hypothesis tests' results, AIC values and graphical diagnostics all show that the GAMs give a better fit than the GLM approach.