Modeling of Motor Vehicle Claims Using Extreme Value Methodology and Monte Carlo Stimulation: A Comparative Study

Abstract

Motor Vehicle Insurance claims form a substantial component of Non life insurance claims and it is also growing with increasing number of vehicles on roads. It is also desirable to have an idea of what will be the likely claim amount for the coming future (Monthly, Quarterly, Yearly) based on past claim data. If one looks at the claim amount one can make out that there will be few large claims compared to large number of average and below average claims. Thus the distributions of claims do not follow a Symmetric pattern which makes it difficult using normal Statistical analysis. The methodology followed to analyze such data is known as Extreme value Analysis. Extreme value analysis is a general name which covers (i) Generalised Extreme Value (GEV) (ii) Generalised Pareto Distribution (GPD). Basically these techniques can deal with non symmetric shape of the distribution which is close to reality. Normally one fits a generalised Extreme Value distribution (GEV)/Generalised Pareto Distribution (GPD) and using parameters of fitted distribution future, forecast of likely losses can be predicted. Second method of analyzing such data is using methodology of simulation. Here we fit a Poisson distribution for arrival of claims and weibull/pareto/Lognormal for claim amount. Using Monte Carlo Simulation one combines both the distributions for future prediction of claim amount. This paper shows a comparison of the above techniques on motor vehicle claims data.