Modeling Frequency and Severity of Insurance Claims in an Insurance Portfolio

James Kiprotich Ng’elechei^1, , Joel Cheruiyot Chelule¹, Herbert Imboga Orango¹ and Ayubu Okango Anapapa²

¹Jomo Kenyatta University of Agriculture and Technology, Department of Statistics and Actuarial Science, Nairobi, Kenya

²University of Eldoret, Department of Mathematics and Computer Science, Eldoret, Kenya

Cite this paper:
James Kiprotich Ng’elechei, Joel Cheruiyot Chelule, Herbert Imboga Orango and Ayubu Okango Anapapa. Modeling Frequency and Severity of Insurance Claims in an Insurance Portfolio. American Journal of Applied Mathematics and Statistics. 2020; 8(3):103-111. doi: 10.12691/ajams-8-3-4

Abstract

Premium pricing is always a challenging task in general insurance. Furthermore, frequency of the insurance claims plays a major role in the pricing of the premiums. Severity in insurance on the other hand, can either be the amount paid due to a loss or the size of the loss event. For insurer’s to be in a position to settle claims that occur from existing portfolios of policies in future, it is necessary that they adequately model past and current data on claim experience then use the models to project the expected future experience in claim amounts. In addition, non-life insurance companies are faced with problems when modeling claim data i.e selecting appropriate statistical distribution and establishing how well it fits the claimed data. Therefore, the study presents a framework for choosing the most suitable probability distribution and fitting it to the past motor claims data and the parameters are estimated using maximum likelihood method (MLE). The goodness of fit of frequency distributions was checked using the chi-square test and Anderson-Darling tests was applied to severity claim distributions. Best chosen models from frequency models and severity models were used to estimate the expected claim amount per risk in the following year. The study employed AIC to choose between competing models. Pareto and Negative Binomial model best fit severity claims, and frequency claims respectively. The two models were used for projection.

Keywords:
claim frequency claim severity goodness-of-fit tests Maximum Likelihood Estimation (MLE)

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