Designing of Optimal Bonus-malus Systems Based on Individual Characteristics in Automobile Insurance

Abstract

Actuarial Science is the discipline that concerns with uncertain events where the concept of probability and statistics provide for essential instruments in the measurement and management of risks in insurance and nance.A key aspect of the business of insurance is the calculation of the price to pay commonly known as the premium to pay in exchange for the transfer of risk.Many insurance companies charge premiums on the policyholders based only on the claim frequency.That way a policyholder who underwent an accident with a small size of loss will be unfairly punished in comparison to an insured policyholder who had an accident with a large amount of loss.In automobile liability insurance,the policyholders do not all the same risk to have an accident.The premium that is charged to each policyholder has to be proportionate to his/her underlying risk to have an accident. Motivated by this,we consider the design of a model that incorporate both the frequency and and severity components and we suggest a method that deliberate concurrently on the number of claims,the exact size of loss and the individual characteristics. The modeling of claim frequency component is based on Poisson mixtures where the number of claims is distributed according to the negative binomial type I.The severity component is modeled using the exponential mixtures where the the losses are distributed according to a Pareto distribution.Using the Baye’s theorem we get the posterior function for the number of claims and the claim amount component.Considering only the claim frequency the premium was estimated as the mean of the posterior structure function in computing premiums.The premiums based on both frequency and severity component was estimated as the product of the mean of posterior structure function of the frequency and severity component.