Distribution of Loss Severity of Bonus-Malus Systems

Maryam Teimourian; Mohammad Q  Vahidi Asl  and Amir T  Payandeh Najafabadi

doi:10.17485/ijst/2014/v7i7.20

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Distribution of Loss Severity of Bonus-Malus Systems

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2014/v7i7.20

Year: 2014, Volume: 7, Issue: 7, Pages: 981–985

Original Article

Distribution of Loss Severity of Bonus-Malus Systems

Maryam Teimourian^1*, Mohammad Q. Vahidi-Asl² and Amir T. Payandeh Najafabadi²

1 Department of Statistics, College of Science, Tehran Science and Research Branch, Islamic Azad University, Tehran, Iran; teimorymar@gmail.com
2 Department of Statistics, Shahid Beheshti University, G. C. Evin, Tehran, Iran; m-vahidi@sbu.ac.ir, Amirtpayandeh@sbu.ac.ir

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

This paper describes a method for computing the distribution function of the loss severity in a Bonus-Malus system with k levels. A closed form expression for the distribution function of the loss severity by assuming different distributions for claim sizes and claim numbers in each level has been derived. Also, Ruin probability and computing VaR in the system have been given.

Keywords: Bonus-Malus System, Cauchy Residue, Characteristic Function, Distribution of Loss Severity