Estimating Insurance Loss Distributions in General Insurance Contracts: A Case Study in Ghana

Insurance loss modeling concerns the prediction of future claims from policyholders in different risk classes based on past observations of claims made by the policyholders in these classes.It is a fundamental branch of Actuarial science and

one of the cornerstones in general insurance contracts.Loss modeling and its variations have been widely studied by researchers in actuarial science and successfully applied by practisioners. Perhaps one of the most well-known theories along this line is the classical credibility theory, which focuses on the mean loss as a point predictor. The idea first appeared in Whitney(1918) and was further developed in Bühlmann (1967) and Bühlmann and Straub (1970). The basic framework of classical credibility is based on Bayesian statistical decision theory. Specifically, actuaries are seeking a function of the observed losses that minimizes the expected prediction error, which, for squared -error prediction error loss, is the mean of the predictive distribution(Klugman 1992; Bühlmann and Gisler 2005). While the credibility formular given by the classical theory is simple and intuitive, it has some limitations. Most importantly, a point predictor alone does not provide any assessment of uncertainty of risk. Actuarial science has a wider range of the application of probability modeling in the field of insurance. An improvement of methods for reducing actuarial risk in insurance company is effective tool for insurance risk management. While the risk management of insurance company is in

connection with her solvency is a complex and comprehensive problem, its solution starts with statistical modeling of number and amounts of individual claims.

The objective of this paper is to present possibilities of how to obtain appropriate probability model that adequately describe the insurance losses and how to use such the model for the purpose of risk management. Modern computer techniques

and statistical software open up a wide field of practical applications for this aim.

This paper includes application of present methods based on data claim amounts in general insurance.The paper also targets the predictive distribution for the next claim, compared to the estimate of the empirical density function based on the

observed claims. This difference is important, because there is clearly more uncertainty in prediction of future claims than estimation of features of the claim distribution, and ignoring this uncertainty leads to overly optimistic predictions.