Abstract
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.
Highlights
It is becoming increasingly important to understand the nature of the claims acts
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
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
Summary
It is becoming increasingly important to understand the nature of the claims acts. the quantitative discovery of the laws governing the probability of ruin is of major scientific importance, and requires us to tackle the factors that determine the timing of claims. Due to constraints on real world data collection techniques, previous ruin probability models did not provide adequate details on the complex properties of inter-arrival claims. They believed that inter-arrival claims could be based on Poisson processes and that inter-arrival time, or time interval between two successive claims, follows an exponential distribution. We use a case study with 10 years of data from one Egyptian insurance company This behavior-driven by the company shows that Claims inter-arrival time routines can be modeled by non-Poisson processes. The results of this study will provide the ability to simplify the treatment and design of claims behavioral interventions
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