Modeling Bursts and Heavy Tails in Inter-Arrival Claims in Non-Life Insurance

Current insurance models, assuming that inter-arrival time of claims, are distributed randomly and thus well approximated by Poisson processes. Here we provide clear proof that the timing of inter-claims fits by non-Poisson patterns, marked by rapid events, separated by long periods of inactivity. The time of inter-arrival claims will be heavy tailed, most claims will be executed quickly, while a few will have very long waiting times. We will model and analysis of insurance based on claim inter-arrival time, the time interval between two successive claims and the ability to carry out such modeling was limited by a lack of ecologically relevant data collected on claims inter-arrival. We propose a structured process behavior model based on data from Egyptian fire insurance company. Our analysis shows that claim activities can be represented by non-Poisson processes and that the subsequent distribution of inter-arrival activity times follows the Pareto distribution. These results will help researchers understand daily behavioral trends and create more sophisticated predictive models of claims.