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MODELING INSURANCE CLAIM DATA USING PARAMETRIC AND CONVOLUTED MODELS is a well researched Actuarial Science Project Topic, it can be used as a guide or framework for your Academic Research.


For claim actuaries, claim modeling is very crucial since a good understanding and interpretation of loss distribution is the backbone of all the decisions made in the insurance industry regarding premium loading, expected profits, reserve necessary to ensure profitability, and the impact of reinsurance. Using claim data obtained from the Central Bank of Nigeria 2015 bulletin and National Insurers Association digest book, this paper determines the best fit for motor, fire, and general accident claim data and ascertain whether the composite models suggested in the literature perform better than the basic parametric models.

The results show that basic parametric models (lognormal and Pareto) performed better than the composite models in fitting motor claim data. Similarly, the parametric model (lognormal) performed better than composite models in fitting fire claim data and general accident claim data. However, the insurance company should acknowledge that some external factors such as the trend in claim response and reporting as well as changes in future claim amounts as a result of carelessness or carefulness of drivers, need to be considered before embarking on the usage of this result. Conclusively, the modeling process is a paramount step before any decision can be made with regard to future policies in Nigeria Insurance Companies hence more effort must be channeled towards ensuring that the process adopted produces accurate and reliable forecasts.


Probabilistic models are widely used in mathematical finance and actuarial sciences. For the reason of simplicity, the most popular models in these areas usually start with many assumptions and restrictions, which lead to an ideal situation and end up with some fixed distribution for estimated financial and actuarial assets (Hao & Alexander, 2014). Insurance claims modeling is a critical actuarial task in property-casualty insurance. A direct output – the predictive distribution of claims – serves as a foundation in the various actuarial decision-making process. At the individual level, predictive models are used for risk classification and to determine the premium and loadings for each policyholder. At the aggregate level, predictive models quantify the risk of a portfolio or a block of business, which helps insurers choose the appropriate level of risk capital and treaty or facultative reinsurance arrangements (Peng, Xiaoping & Anastasia, 2015).

General insurance is an area developing quickly for actuaries. This includes large commercial risks and liability insurance, health insurance, and personal/property insurance (Boland, 2006). The insurance industry is one of the economic sectors in a country which is of great importance as it is a form of economic remediation. It serves as means of minimizing financial loss due to the consequences of risk by spreading or pooling the risk over a large number of people and to carry out this function as a risk management tool, insurance companies rely on the law of large numbers. This pooling mechanism determines the unique semi-continuous feature of insurance claim data (Peng, Xiaoping & Anastasia, 2015).

Insurance, as an industry is driven by data with the main fund outflow being the claim payment, make use of a large number of analysts including actuaries so as to understand the claim data. Claim actuaries focus less on the occurrence of the claims rather they show keen interest in the severity of the claims. That is, they are concern with the amount of money the insurance company will have to pay but show less concern for the circumstance that gives rise to the claim frequency. Hence, general insurance actuaries must have a strong knowledge of various models for the number of claims payable by an insurance company.

The severity of claims in terms of costs faced by insurers is a mixture of moderate and large claims. Modeling insurance loss data of a unimodal type with a heavy tail has been an interesting topic for actuaries. Distributions that can mimic the heavy tail of the insurance loss data are crucial to sufficiently provide a good estimate of the associated business risk level (Abubakar, Hamzah, Maghsoudi & Nadarajah, 2015). In this situation, Pareto distribution had been used to model the larger loss data by researchers in the past. But when claims are made of smaller data with high occurrences and large losses with low occurrences, other continuous parametric families like gamma, lognormal, exponential, and Weibull can be used (Enrique & Chun, 2011).

Nevertheless, no standard parametric model seems to provide an acceptable fit for both small and large claims since probability distributions that provide a good fit for the head can be particularly bad at fitting the tail. And to overcome this, composite parametric models that use Lognormal (see Cooray & Ananda, 2005), Weibull (see Ciumara, 2006) or Exponential (see Sandra & Raluca, 2006) up to an unknown single threshold value θ, estimated from data and a two-parameter Pareto density thereafter have been considered. Two-piece composite distributions arise in many areas of the sciences. The first two-piece composite distribution with each piece described by a normal distribution appears to have been used by Gibbons & Mylroie (1973). Recently, two-piece composite distributions with the first piece described a lognormal distribution (which we refer to as composite lognormal distributions) have proved popular in insurance and related areas.

Cooray & Ananda (2005) models the head and tail by weighted lognormal and Pareto distributions, respectively, and show better fit to real skewed loss data than several standard models. They also employ the continuity and differentiability conditions at the threshold, θ, to ensure that the resulting models are both continuous and smooth. Scollnik (2007) improved the composite lognormal–Pareto model by allowing flexible mixing weights, replacing a constant weight applied by Cooray & Ananda (2005), resulting in a better fit to the loss data. He reiterates this fact using the composite Weibull–Pareto model in Scollnik & Sun (2012).
In Nigeria, as well as other developing economies, there is a paucity of data. Further, there is little analysis of the existing data beyond the simple descriptive statistics that organizations like the Nigerian Insurance Association annually conduct. This probably explains why insurance companies in such economies are not operating at their full potential. Claims, especially large ones, had been the Achilles‟ heels of the insurance industry as past incidents of repudiation of claims had created an image problem for the industry. An analysis of claim size is essential in determining actually fair premium (Adeleke & Ibiwoye, 2011).
For claim actuaries, claim modeling is very crucial since a good understanding and interpretation of loss distribution is the backbone of all the decisions made in the insurance industry regarding premium loading, expected profits, reserve necessary to ensure profitability, and impact of re-insurance (Boland, 2006). But despite the fact that insurance companies in Nigeria record an overwhelming number of claims in any given period, there has been little or no analysis of those claim data beyond simple descriptive statistics that is done annually by organizations like Nigeria Insurance Association and this is an indicator that Insurance sector of Nigeria economy is not operating at its full potential.

And for it to operate fully the analysis must go beyond the descriptive statistics hence the understanding of the probability and loss distributions is essential for the general insurance actuaries so as to be able to summarize and model a large amount of claim data and give timely outcome. These loss distributions are a ‘‘must-have’’ tools for any assessment done actuarially and that is why this study had described loss distributions and emphasized their properties.


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