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Joint optimization of transition rules and the premium scale in a bonus-malus system
Recurso electrónico / Electronic resource
MAP20200029724
Csaba Ágoston, Kolos ‌
Joint optimization of transition rules and the premium scale in a bonus-malus system / Kolos Csaba Ágoston, Márton Gyetvai
Sumario: Bonus-malus systems (BMSs) are widely used in actuarial sciences. These systems are applied by insurance companies to distinguish the policyholders by their risks. The most known application of BMS is in automobile third-party liability insurance. In BMS, there are several classes, and the premium of a policyholder depends on the class he/she is assigned to. The classification of policyholders over the periods of the insurance depends on the transition rules. In general, optimization of these systems involves the calculation of an appropriate premium scale considering the number of classes and transition rules as external parameters. Usually, the stationary distribution is used in the optimization process. In this article, we present a mixed integer linear programming (MILP) formulation for determining the premium scale and the transition rules. We present two versions of the model, one with the calculation of stationary probabilities and another with the consideration of multiple periods of the insurance. Furthermore, numerical examples will also be given to demonstrate that the MILP technique is suitable for handling existing BMSs
En: Astin bulletin. - Belgium : ASTIN and AFIR Sections of the International Actuarial Association = ISSN 0515-0361. - 01/09/2020 Volumen 50 Número 3 - septiembre 2020 , p. 743-776
1. Cálculo actuarial ‌. 2. Bonus-malus ‌. 3. Ciencias Actuariales y Financieras ‌. 4. Asegurados ‌. 5. Primas de seguros ‌. 6. Cálculo de probabilidades ‌. I. Gyetvai, Márton ‌. II. Título.