Claims modeling with and alternative gamma-exponentiated weibull distribution and ruinprobability approximation

Abstract

In this dissertation, two studies that are beneficial for actuaries and the insurance business are proposed. In the first study, an exponentiated Weibull distribution using gamma-generated distribution is modified to obtain an alternative gamma-exponentiated Weibull (AGEW) distribution; its sub-models include both gamma and Weibull distributions, both of which are popular in claims modeling by insurance companies. Its basic structural properties such as distribution function, density function, and moments were investigated. Moreover, the maximum likelihood method to estimate the AGEW distribution’s parameters was utilized, then the distribution was applied to a real-life dataset to show its superiority over gamma and Weibull distributions by comparing fitness between them

In the second study, a new approximation method to obtain the ruin probability referring to the risk of insolvency of an insurance company is proposed by modifying the Pollaczek-Khinchin approximation. The proposed approximation is simpler and requires fewer assumptions than other methods mentioned in the literature. The results from a simulation study show that, in some cases, the proposed method gave better approximated ruin probability values in terms of the overall deviation from the exact values. Insurance companies are interested in calculating the initial capital using ruin probability, and so with this in mind, the proposed method was applied to estimate the minimum initial capital that needs to be reserved to ensure that the ruin probability does not exceed an acceptable quantity. To illustrate the performance of the approximation, the ruin probability and the minimum initial capital modeled by the AGEW distribution were estimated with a real-life dataset.