Title: Designing an optimal bonus-malus system using the number of reported claims, steady-state distribution, and mixture claim size distribution

Authors: Amir T. Payandeh Najafabadi; Mansoureh Sakizadeh

Addresses: Department of Mathematical Sciences, Shahid Beheshti University, G.C. Evin, 1983963113, Tehran, Iran ' Department of Mathematical Sciences, Shahid Beheshti University, G.C. Evin, 1983963113, Tehran, Iran

Abstract: This article, in a first step, considers two Bayes estimators for the relativity premium of a given bonus-malus system. It then develops a linear relativity premium that closes, in the sense of weighted mean square error loss, to such Bayes estimators. In a second step, it supposes that the claim size distribution for a given bonus-malus system can be formulated as a finite mixture distribution. It then evaluates the base premium under a Bayesian framework for such a finite mixture distribution. The Loimaranta efficiency of such a linear relativity premium, for several bonus-malus systems, has been compared with two Bayes and ordinary linear relativity premiums.

Keywords: bonus-malus system; relativity premium; Bayes estimator; weighted mean square error; Loimaranta efficiency.

DOI: 10.1504/IJISE.2019.101117

International Journal of Industrial and Systems Engineering, 2019 Vol.32 No.3, pp.304 - 331

Received: 08 May 2017
Accepted: 09 Oct 2017
Published online: 24 Jul 2019 *

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