Centro de Documentacion de Fundación MAPFRE - Stationary probabilities and the monotone likelihood ratio in bonus-malus systems

Notas: Sumario: This paper examines bonusmalus systems (BMS) and demonstrates that their stationary probabilities satisfy the monotone likelihood ratio property (MLRP), a key feature that explains why higher-risk policyholders tend to remain in higher premium classes, while lower-risk individuals migrate toward lower premiums. Focusing on BMS models represented by an ergodic Markov chain with a +1/d transition rule and at most one claim per period, the authors establish the MLRP using linear recurrences derived from the stationary distributionan analytical approach not previously applied in this context. The study also highlights an important practical implication: in bonusmalus design problems, the premium scale becomes automatically monotonic when this property holdsRegistros relacionados: En: Astin bulletin. - Belgium : ASTIN and AFIR Sections of the International Actuarial Association = ISSN 0515-0361. - 19/01/2026 Volume 56 Issue 1 - January 2026 , p. 89 - 100Materia / lugar / evento: Seguro de automóviles Tarificación Bonus-malus Matemática del seguro Modelos matemáticos Estadística matemática Cálculo actuarial Otros autores: Papp, Dávid
International Actuarial Association
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