de Lourdes Centeno, Maria; Andrade e Silva, João Manuel Optimal bonus scales under path-dependent bonus rules. (English) Zbl 1015.62103 Scand. Actuar. J. 2002, No. 2, 129-136 (2002). 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)].. Reviewer: N.M.Zinchenko (Kyïv) Cited in 1 Document MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B30 Risk theory, insurance (MSC2010) Keywords:bonus systems; Markov chains; bonus scale Citations:Zbl 0682.62085 PDF BibTeX XML Cite \textit{M. de Lourdes Centeno} and \textit{J. M. Andrade e Silva}, Scand. Actuar. J. 2002, No. 2, 129--136 (2002; Zbl 1015.62103) Full Text: DOI OpenURL References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.