An Application of Survival Analysis in Auto Insurance Contracts in Ghana

Abstract

Survival models for life-time data and other time-to-event data are widely used in many fields, including medicine, economics, agriculture and actuarial mathematics. In this study, survival analysis was applied to the Ghanaian insurance industry to model the time until first claim after policy inception and time until payment after reporting. The nonparametric Kaplan-Meier model is used in the analysis. Cumulative hazard functions for time until claim reporting and time until payment were calculated. Confidence intervals were also computed for the Kaplan-Meier estimates. The findings indicate that time until reporting claims and time until payment followed a polynomial of order 6. It was also observed that the log-transformed confidence interval is better than the linear confidence interval. The probability that claims will be reported within a shorter period (e.g. a week) was higher than that of a longer period (e.g. a month). It was concluded that survival analysis is an appropriate tool for studying the insurance industry.