Designing an Optimal Collision Premium Model with Emphasis on the Effect of Macroeconomic Variables on the Demand Function

Determining a fair premium is an essential issue for insurance companies. Many premium models are based on risk analysis and market behavior. Risk analysis is divided into Priori pricing and Posteriori pricing. These models use claim frequency and claim severity. Market behavior models include some variables affecting the demand function to determine premium. In contrast, insurance companies involve with uninsurable risks such as economic risks in collision insurance, and the insurance premium depends on the price of competitors, because there are competitive insurance environments. Therefore, it is essential to consider macroeconomic variables in the demand function. This study, for the first time, includes the insurance penetration in the demand function. To achieve the goal, the researcher has selected a private company active in the insurance industry for sampling. The method used was based on stochastic dynamic programming. The wealth equation of the insurance company is determined based on the Markov process, and the objective function of the model is a quadratic form. The Demand function is described as a function of macroeconomic parameters such as elasticity of demand, inflation rate, and insurance penetration. The optimal premium is calculated for different levels of market premium. The results show the average premium of the market becomes bigger, the optimal premium becomes lower.