An alternative approach to bonus malus

Gracinda Rita Guerreiro; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2004)

  • Volume: 24, Issue: 2, page 197-213
  • ISSN: 1509-9423

Abstract

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Under the assumptions of an open portfolio, i.e., considering that a policyholder can transfer his policy to another insurance company and the continuous arrival of new policyholders into a portfolio which can be placed into any of the bonus classes and not only in the "starting class", we developed a model (Stochastic Vortices Model) to estimate the Long Run Distribution for a Bonus Malus System. These hypothesis render the model quite representative of the reality. 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.

How to cite

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Gracinda Rita Guerreiro, and João Tiago Mexia. "An alternative approach to bonus malus." Discussiones Mathematicae Probability and Statistics 24.2 (2004): 197-213. <http://eudml.org/doc/287595>.

@article{GracindaRitaGuerreiro2004,
abstract = {Under the assumptions of an open portfolio, i.e., considering that a policyholder can transfer his policy to another insurance company and the continuous arrival of new policyholders into a portfolio which can be placed into any of the bonus classes and not only in the "starting class", we developed a model (Stochastic Vortices Model) to estimate the Long Run Distribution for a Bonus Malus System. These hypothesis render the model quite representative of the reality. 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.},
author = {Gracinda Rita Guerreiro, João Tiago Mexia},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {bonus malus; stochastic vortices; long run distribution; optimal bonus scales; optimal bonus scales.},
language = {eng},
number = {2},
pages = {197-213},
title = {An alternative approach to bonus malus},
url = {http://eudml.org/doc/287595},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Gracinda Rita Guerreiro
AU - João Tiago Mexia
TI - An alternative approach to bonus malus
JO - Discussiones Mathematicae Probability and Statistics
PY - 2004
VL - 24
IS - 2
SP - 197
EP - 213
AB - Under the assumptions of an open portfolio, i.e., considering that a policyholder can transfer his policy to another insurance company and the continuous arrival of new policyholders into a portfolio which can be placed into any of the bonus classes and not only in the "starting class", we developed a model (Stochastic Vortices Model) to estimate the Long Run Distribution for a Bonus Malus System. These hypothesis render the model quite representative of the reality. 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.
LA - eng
KW - bonus malus; stochastic vortices; long run distribution; optimal bonus scales; optimal bonus scales.
UR - http://eudml.org/doc/287595
ER -

References

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  1. [1] 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. 
  2. [2] Ø. Borgan, J. Hoem and R. Norberg, A non asymptotic criterion for the evaluation of automobile bonus system, Scandinavian Actuarial Journal (1981), 165-178. Zbl0476.62080
  3. [3] L. Centeno and J. Andrade e Silva, Bonus systems in open portfolio, Insurance Mathematics e Economics (2001), 341-350. Zbl1055.91021
  4. [4] H. Cramer, Mathematical Methods of Statistics, Princeton University Press 1957. 
  5. [5] V. Gilde and B. Sundt, On bonus systems with credibility scales, Scandinavian Actuarial Journal (1989), 13-22. Zbl0682.62085
  6. [6] G. Guerreiro, Uma Abordagem Alternativa para Bonus Malus, Instituto Superior de Economia e Gestão (In Portuguese) 2001. 
  7. [7] M. Healy, Matrices for Statistics, Oxford Science Publications 1986. 
  8. [8] J. Lemaire, Bonus-Malus Systems in Automobile Insurance, Kluwer Academic Publishers 1995. 
  9. [9] J. Mexia, Vórtices Estocásticos de Pargmetro Discreto, Comunication in the III Actuarial Colloquium FCT-UNL (In Portuguese) 1999. 
  10. [10] E. Parzen, Stochastic Processes, Holden Day, S. Francisco 1965. 
  11. [11] E. Seneta, A Non-Negative Matrices and Markov Chains Springer-Verlag 1981. 

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