Two possible applications of nonlinear regression models in insurance are discussed. The first part deals with modelling IBNR reserves when a cubic approximation to the solution locus is used instead of linear or quadratic ones. A formula is given for construction of improved confidence regions for parameters in such models.Using this approach IBNR reserves for a data set are computed.In the second part a method is proposed of how to measure the influence of additive perturbations on nonlinear regression model parameters. An example is given which shows how this method can be used to preserve privacy of sensitive data in insurance business.