Optimal bonus scales under path-dependent bonus rules. (English) Zbl 1015.62103

The authors study bonus systems that are not first order Markovian processes, but can be regarded as Markovian simply by increasing the number of space states of the system. Examples of this kind of bonus malus systems are the systems in Belgium, France, Luxemburg, and the old system in Portugal. Thus, the optimal scales for such systems are deduced using the approach developed for Markov type bonus systems, for example, in papers by R. Norberg [Scand. Actuar. J. 1976, 92-107 (1976); ibid., 182 (1976)], or by V. Gilde and B. Sundt [ibid. 1989, No. 1, 13-22 (1989; Zbl 0682.62085)]..


62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)


Zbl 0682.62085
Full Text: DOI


[1] Borgan O., Scandinavian Actuarial Journal pp 165– (1981)
[2] DOI: 10.1016/S0167-6687(00)00082-2 · Zbl 1055.91021
[3] Gilde V., Scandinavian Actuarial Journal 1 pp 13– (1989) · Zbl 0682.62085
[4] Lemaire J., Bonus-malus systems in automobile insurance (1995)
[5] Norberg R., Scandinavian Actuarial Journal 2 pp 92– (1976) · Zbl 0337.62071
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