ReviewNonparametric estimation of the claim amount in the strong stability analysis of the classical risk model

This paper presents an extension of the strong stability analysis in risk models using nonparametric kernel density estimation for the claim amounts. First, we detail the application of the strong stability method in risk models realized by V. Kalashnikov in 2000. In particular, we investigate the conditions and the approximation error of the real model, in which the probability distribution of the claim amounts is not known, by the classical risk model with exponentially distributed claim sizes. Using the nonparametric approach, we propose different kernel estimators for the density of claim amounts in the real model. A simulation study is performed to numerically compare between the approximation errors (stability bounds) obtained using the different proposed kernel densities.