Discussiones Mathematicae Probability and Statistics 24(2) (2004) 197-213
Gracinda Rita Guerreiro and João Tiago Mexia
Department of Mathematics
FCT - New University of Lisbon
Quinta da Torre, 2829-516 Caparica, Portugal
With the obtained Long Run Distribution, a few optimal bonus scales were calculated, such as Norberg's (1979), Borgan, Hoem's and Norberg's (1981), Gilde and Sundt's (1989) and Andrade e Silva's (1991).
To compare our results, since this was the first application of the model, we used the Classic Model for Bonus Malus and the Open Model developed by Centeno and Andrade e Silva (2001).
The results of the Stochastic Vortices and the Open Modelare highly similar and quite different from those of the Classic Model. Besides this the distribution of policyholders in the various bonus classes was derived assuming that the entrances followed adequatestochastic models.
Keywords: bonus malus, stochastic vortices, long run distribution, optimal bonus scales.
2000 Mathematics Subject Classification: 60J05, 60J20.
|||J. Andrade e Silva, Estruturas Tarifárias nos Ramos Reais da Indústria Seguradora - Uma Aplicação ao sector automóvel em Portugal, Instituto Superior de Economia e Gestão (In Portuguese) 1991.|
|||Ø. Borgan, J. Hoem and R. Norberg, A non asymptotic criterion for the evaluation of automobile bonus system, Scandinavian Actuarial Journal (1981), 165-178.|
|||L. Centeno and J. Andrade e Silva, Bonus systems in open portfolio, Insurance Mathematics e Economics (2001), 341-350.|
|||H. Cramer, Mathematical Methods of Statistics, Princeton University Press 1957.|
|||V. Gilde and B. Sundt, On bonus systems with credibility scales, Scandinavian Actuarial Journal (1989), 13-22.|
|||G. Guerreiro, Uma Abordagem Alternativa para Bonus Malus, Instituto Superior de Economia e Gestão (In Portuguese) 2001.|
|||M. Healy, Matrices for Statistics, Oxford Science Publications 1986.|
|||J. Lemaire, Bonus-Malus Systems in Automobile Insurance, Kluwer Academic Publishers 1995.|
|||J. Mexia, Vórtices Estocásticos de Parâmetro Discreto, Comunication in the III Actuarial Colloquium FCT-UNL (In Portuguese) 1999.|
|||E. Parzen, Stochastic Processes, Holden Day, S. Francisco 1965.|
|||E. Seneta, A Non-Negative Matrices and Markov Chains Springer-Verlag 1981.|
Received 7 January 2004
Revised 18 October 2004