Calculation of the relative premium of a rate system based on the Poisson model at two points

Payandeh NajafAbadi, A.T.; Atatalab, F.; Rezazadeh, R.

doi:10.22056/ijir.2019.02.01

Document Type : Original Research Paper

Authors

Department of Actuarial Science, Shahid Beheshti University, Tehran, Iran

https://doi.org/10.22056/ijir.2019.02.01

Abstract

Purpose: One of the most important issues faced by insurance companies is determining fair premiums. Due to the fact that the record of no loss leads to a discount in the insurance premium, we assume that the insurers present a special behavior in two points i and j. In such a way that the frequency of two points i and j in the observations is significantly high. The purpose of this article is to estimate the relative premium in the rate system under the accumulated Poisson models at these two points.
Methodology: In this research, a Poisson distribution is used to model the desire for reward at two points i and j. The method used is an approximate method based on Bayesian methods for reliable estimators under two loss functions of squared error and Linex.
Findings: The obtained numerical results indicate that if we use the Poisson models at two points, the relative premium will decrease significantly, which has a significant effect on attracting more customers. It was also shown that using the Linux loss function is a good idea to reduce the relative premium of customers.
Conclusion: In a rated system, the insurance records of an insured are used to calculate the fair premium. The issue that was researched in this article is the modeling of insurers' willingness to receive discounts based on not reporting small claims.
The results of this article showed: (1) if we model the phenomenon of customers' willingness to reward using Poisson models, the relative premium rate will decrease significantly; (2) The relative premium estimator under the Lionx loss function is lower than the relative premium under the error squared loss function.

Considering that the reward-penalty system is based on the number of damages, it cannot be a fair system, so it is recommended to use a system that involves both the number and severity of damages in the calculations.

Keywords

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Iranian Journal of Insurance Research

Calculation of the relative premium of a rate system based on the Poisson model at two points

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Volume 8, Issue 2 - Serial Number 28
April 2019
Pages 74-89

Calculation of the relative premium of a rate system based on the Poisson model at two points

Letters to Editor

Send comment about this article

Volume 8, Issue 2 - Serial Number 28April 2019Pages 74-89

Volume 8, Issue 2 - Serial Number 28
April 2019
Pages 74-89