Abstract:
Claims experience in non-life insurance is contingent on random eventualities
of claim frequency and claim severity. By design, a single policy may possibly
incur more than one claim such that the total number of claims as well as the
total size of claims due on any given portfolio is unpredictable. For insurers to
be able to settle claims that may occur from existing portfolios of policies at
some future time periods, it is imperative that they adequately model historical
and current data on claims experience; this can be used to project the expected
future claims experience and setting sufficient reserves. Non-life insurance
companies are often faced with two challenges when modeling claims
data; selecting appropriate statistical distributions for claims data and establishing
how well the selected statistical distributions fit the claims data. Accurate
evaluation of claim frequency and claim severity plays a critical role in
determining: An adequate premium loading factor, required reserve levels,
product profitability and the impact of policy modifications. Whilst the assessment
of insurers’ actuarial risks in respect of their solvency status is a
complex process, the first step toward the solution is the modeling of individual
claims frequency and severity. This paper presents a methodical framework
for choosing a suitable probability model that best describes automobile
claim frequency and loss severity as well as their application in risk management.
Selected statistical distributions are fitted to historical automobile
claims data and parameters estimated using the maximum likelihood method.
The Chi-square test is used to check the goodness-of-fit for claim frequency
distributions whereas the Kolmogorov-Smirnov and Anderson-Darling tests
are applied to claim severity distributions. The Akaike information criterion
(AIC) is used to choose between competing distributions. Empirical results
indicate that claim severity data is better modeled using heavy-tailed and
skewed distributions. The lognormal distribution is selected as the best distribution
to model the claim size while negative binomial and geometric dis-tributions are selected as the best distributions for fitting the claim frequency
data in comparison to other standard distributions.