IMPROVING GLOBAL ELASTICITY OF BONUS-MALUS SYSTEM

• Authors: Topolewski Marcin , Bernardelli Michał
• Languages of publication: EN

Abstracts

EN

We optimize transition rules of bonus-malus system to achieve possibly best premium elasticity as defined by Loimaranta [1972] and later generalized as global elasticity by De Pril (1978). We use premium scale given by Norberg (1976). This issue constitutes a nonlinear nonconvex discrete optimization problem. To solve this problem, we apply improved greedy optimization algorithm, similar to one proposed by Morlock (1984). We analyse systems of different size for portfolios characterized by inverse Gaussian risk structure function with various parameters. We also propose alternative measures of global elasticity.

Keywords

EN

bonus-malus system; transition rules; optimization; premium elasticity; automobile insurance

• Publisher: Katedra Ekonometrii i Statystyki, Szkoła Główna Gospodarstwa Wiejskiego w Warszawie
• Journal: Metody Ilościowe w Badaniach Ekonomicznych
• Year: 2017
• Volume: 18
• Issue: 1
• Pages: 120-133

Contributors

author

Topolewski Marcin

• Collegium of Economic Analysis, Warsaw School of Economics - SGH, Poland

author

Bernardelli Michał

• Collegium of Economic Analysis, Warsaw School of Economics - SGH, Poland

References

• Borgan O., Hoem J.M., Norberg R. (1981) A Nonasymptotic Criterion for Evaluation of Automobile Bonus System. Scandinavian Actuarial Journal, 165-178.
• De Pril N. (1978) The Efficiency of a Bonus-Malus System. ASTIN Bulletin, 10, Part 1, 59-72.
• Gilde V., Sundt B. (1989) On Bonus Systems with Credibility Scale. Scandinavian Actuarial Journal, 13-22.
• Lemaire J. (1985) Automobile Insurance: Actuarial Models. Kluwer Nijhoff, Boston.
• Lemaire J. (1995) Bonus-malus Systems in Automobile Insurance. Kluwer Nijhoff, Boston.
• Lemaire J., Zi H. (1994) High deductibles instead of bonus-malus. Can it work? Astin Bulletin, 24 (1), 75–86.
• Loimaranta K. (1972) Some Asymptotic Properties of Bonus Systems. ASTIN Bulletin, VI, Part 3, 233–245.
• Morlock M. (1985) Aspects of optimization in automobile insurance. Contributions to Operations Research, Springer-Verlag, 240, 131–141.
• Norberg R. (1976) A credibility theory for automobile bonus systems. Scandinavian Actuarial Journal, 92–107.
• Podgórska M., Cieślik B., Kryszeń B., Niemiec M., Topolewski M. (2006) System bonus-malus sprawiedliwy w sensie przejść między klasami. Instytut Ekonometrii SGH, Warszawa.
• Kemeny J., Snell J. (1976) Finite Markov Chains. Springer-Verlag.
• Topolewski M., Bernardelli M. (2015) Optymalizacja reguł przejścia systemu bonus-malus o składkach Q-optymalnych. Roczniki Kolegium Analiz Ekonomicznych, 37, 229-252.
• Willmot G. (1987) The Poisson-Inverse Gaussian Distribution as an Alternative to the Negative Binomial. Scandinavian Actuarial Journal, 113–127.