Modal Interval Probability: Application to Bonus-Malus Systems

Author:

Adillon Romàn1ORCID,Jorba Lambert1,Mármol Maite1

Affiliation:

1. Departament de Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Av. Diagonal, 690, 08034 Barcelona, Spain

Abstract

Classical intervals have been a very useful tool to analyze uncertain and imprecise models, in spite of operative and interpretative shortcomings. The recent introduction of modal intervals helps to overcome those limitations. In this paper, we apply modal intervals to the field of probability, including properties and axioms that form a theoretical framework applied to the Markovian analysis of Bonus-Malus systems in car insurance. We assume that the number of claims is a Poisson distribution and in order to include uncertainty in the model, the claim frequency is defined as a modal interval; therefore, the transition probabilities are modal interval probabilities. Finally, the model is exemplified through application to two different types of Bonus-Malus systems, and the attainment of uncertain long-run premiums expressed as modal intervals.

Publisher

World Scientific Pub Co Pte Lt

Subject

Artificial Intelligence,Information Systems,Control and Systems Engineering,Software

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