| dc.description.abstract | The main purpose of this project was to design an optimal bonus malus system that incorporates
both the number of claims and the claim size. Majority of insurance companies charge premiums
based on the number of accidents. This way a policyholder who had an accident with a small size
of loss is penalized in the same way with a policyholder who had an accident with a big size of
loss, thus the need to develop a model that incorporates both the frequency and the severity
components. The frequency component was modelled using Poisson mixtures where the number
of claims is Poisson distributed and the underlying risk for each policyholder or group of
policyholders is the mixing distribution. We considered the mixing distribution to be gamma,
exponential, Erlang and Lindely distribution. For the severity component we used exponential
gamma mixture (Pareto distribution) where the claim amount is exponential distributed and the
mean claim amount is inverse Gamma. Using the Bayes theory we obtain the posterior structure
function for the frequency and the severity component. The premium was estimated as the mean
of the posterior structure function for the frequency component if we compute premiums based on
the number of claims only. The premium based on both frequency and severity components was
estimated as the product of the mean of the posterior structure function of the frequency component
and the mean of the posterior structure function of the severity component. We applied the data
presented by Walhin and Paris (2000) with some adjustment of the claim amount data to fit the
Pareto distribution. The study established that if we consider only the frequency component, the
system was unfair to policyholders with small claim amounts. However optimal BMS based on
frequency and severity component was found to be fair to all policyholder since policyholders with
large claim amounts were charged higher malus due to the risk they pose to portfolio. Therefore
we recommend a system that considers both frequency and severity components.
Keywords. BMS, Poisson mixtures, exponential mixtures, frequency component, severity
component. | en_US |
