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.
Publisher
University of Nairobi
Rights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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