Influence functions of empirical nonparametric estimators of net reinsurance premiums

In this paper we illustrate the usefulness of influence functions for studying robustness properties of empirical nonparametric estimators of net premiums of various reinsurance treaties. (Proportional, stop-loss, excess-of-loss, largest claims, and excédent du coût moyen relatif (ecomor) type reinsurance treaties are considered.) We use the gross error sensitivity (GES) and the upper breakdown point (UBP) as robustness criteria. It is found that empirical nonparametric estimators are not robust with respect to GES and UBP. Alternative methods of estimation are suggested.