RESEARCH ARTICLE


Nonlinear Regression Models with Applications in Insurance



Rastislav Potockỳ, Milan Stehlík*
Department of Applied Mathematics and Statistics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava 4, Slovak Republic.


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© 2010 Potockỳ et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Applied Mathematics and Statistics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava 4, Slovak Republic. Tel:+43 732 2468 5881; Fax: +43 732 2468 9846; E-mails: mlnstehlik@gmail.com ,Milan.Stehlik@jku.at


Abstract

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.

Keywords: Nonlinear regression models, confidence regions, additive perturbations, IBNS reserves, privacy of data..