Calculation of the Relative Premium based on Two-Point Inflated Poisson Model for Rate-Making System

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Payandeh NajafAbadi Amir Teimour; Atatalab Fatemeh; REZAZADEH RAMEZAN

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Paper Information

Journal: IRANIAN JOURNAL OF INSURANCE RESEARCH (SANAAT-E-BIMEH) Year:2019 | Volume:34 | Issue:2 (134) Page(s): 7-27

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Title

Calculation of the Relative Premium based on Two-Point Inflated Poisson Model for Rate-Making System

Author(s)

Payandeh NajafAbadi Amir Teimour | Atatalab Fatemeh | REZAZADEH RAMEZAN | Issue Writer Certificate

Keywords

Relative premiumQ1

Inflated Poisson distributionQ1

Linear credibilityQ1

Loss functionQ1

Abstract

Objective: One of the most important issues facing insurance companies is the determination of fair premium. Since no claims history leads to a reduction in the premium, in this study we assume that insureds have some sort of censored behavior at two points i and j. The frequency of two points i and j is significantly high in the observations. In this paper, we use an Inflated Poisson distribution of two points i and j to estimate Relative premium in Bonus-Malus system. Methodology: In this paper we use i-j inflated Poisson model for modeling hunger for bonus. The method used is an approximation based on Bayesian methods for estimators of credibility under quadratic and LINEX Loss functions. Findings: The numerical results show that if we model the phenomenon of customer hunger for bonus using two-point inflated Poisson models, the Relative premium is significantly reduced which attracts customers. In addition, it is also shown that using the LINEX Loss function is a suitable method to reduce the Relative premium of customers. Conclusion: In a rating system, an insurer's insurance records are used to calculate fair premiums. The problem addressed in this paper is modeling hunger for bonus based on non-reporting of small losses. The results of the present paper show that: (1) Relative premium is significantly reduced when modeling hunger for bonus by using inflated Poisson models; (2) Relative premium estimator under LINEX Loss function is less than this premium under quadratic Loss function. Since Bonus-Malus system is based on number of claims, it cannot be a fair system, so it is recommended to use a system that incorporates both the number and severity of claims into the calculations.

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APA: Copy

Payandeh NajafAbadi, Amir Teimour, Atatalab, Fatemeh, & REZAZADEH, RAMEZAN. (2019). Calculation of the Relative Premium based on Two-Point Inflated Poisson Model for Rate-Making System. IRANIAN JOURNAL OF INSURANCE RESEARCH (SANAAT-E-BIMEH), 34(2 (134) ), 7-27. SID. https://sid.ir/paper/383943/en

Vancouver: Copy

Payandeh NajafAbadi Amir Teimour, Atatalab Fatemeh, REZAZADEH RAMEZAN. Calculation of the Relative Premium based on Two-Point Inflated Poisson Model for Rate-Making System. IRANIAN JOURNAL OF INSURANCE RESEARCH (SANAAT-E-BIMEH)[Internet]. 2019;34(2 (134) ):7-27. Available from: https://sid.ir/paper/383943/en

IEEE: Copy

Amir Teimour Payandeh NajafAbadi, Fatemeh Atatalab, and RAMEZAN REZAZADEH, “Calculation of the Relative Premium based on Two-Point Inflated Poisson Model for Rate-Making System,” IRANIAN JOURNAL OF INSURANCE RESEARCH (SANAAT-E-BIMEH), vol. 34, no. 2 (134) , pp. 7–27, 2019, [Online]. Available: https://sid.ir/paper/383943/en

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