7 ﺳﺎل ﺳﯽ و ﭼﻬﺎرم. ﺗﺎﺑﺴﺘﺎن1398 . ﺷﻤﺎره2 ﻓﺼﻠﻨﺎﻣﻪ ﭘﮋوﻫﺸﻨﺎﻣﻪ ﺑﯿﻤﻪ Calculation of the Relative Premium based on Two-Point Inflated Poisson Model for Rate-Making System Amir Teimour Payandeh NajafAbadi  Fatemeh Atatalab Ramezan Rezazadeh 1-Professor, Shahid Beheshti University. 2-Ph.D Student in Actuarial Science, Shahid Beheshti University. 3-Master of Actuarial Science, Shahid Beheshti University. 10.22056/jir.2019.139100.2326 ): DOI ( 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. Received: 2018 July 18 Accepted: 2019 August 26 Keywords: Relative premium, Inflated Poisson distribution, Linear credibility, Loss function. JEL Classification: G22, C11, C13  Corresponding Author: Amir Teimour Payandeh NajafAbadi Email: Amirtpayande@sbu.ac.ir Journal of Insurance Research