An Actuarial Model Based On The Composite Exponential-Pareto Distribution And Its Application In Insurance

Log-Normal distribution is always used by insurance companies to model actuarial data, esp. for large losses or reinsurance payments. However, insurance payment data are typically highly positively skewed and distributed with large upper tail. In this context using the Log-Normal model for actuarial data brings about a disadvantage that it well covers the behavior of small losses, but fails to cover large ones. Therefore, premium calculated under this model is underestimated, which could incur losses for the insurance company or even lead to bankruptcy.We propose a new model for actuarial data, composing two distributions. By taking into account the tail behavior of both small and large losses, we combine two distributions in which exponential density fits small losses while Pareto density fits large ones. By seeking an unknown threshold value, we finally find a fine smooth density function called the composite exponential-Pareto model with one parameter. The resulting density has a larger tail than the exponential density.The outline of the paper is as follows. In section one, a brief introduction of research background and previous findings is given. In section two, we present the derivation of the composite exponential-Pareto model and discuss its properties and behavior by illustrating its density functions. In section three, we discuss the maximum likelihood parameter estimation methods and use Matlab simulating software to verify the accuracy of our finding.The composite exponential-Pareto model not only serves as a guiding principle for insurance companies in calculating premiums, but also works on VaR measurement. As insurance industry mingles with financial market in a step-by-step manner, may managers draw inspiration from this composite exponential-Pareto model in risk management and scientific corporate operation.