The Impact of Previous Claims on the Future Claims: An Application to the French Automobile Insurance Market

• Activity Number: 509
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Risk Analysis
• Author(s): Michel Grun-Rehomme*+
• Companies: University Paris-Pantheon
• Keywords: Solvency ; ERM ; ORSA ; Risk Appetite

Abstract

The risk of each insured motor vehicle is not predictable and is known only retrospectively. Unlike the collective risk is predictable when we have the experience of the past later observed over a relatively large population comparable to the existing portfolio. In this study, we would like to examine empirically on data from a French insurer, if the accident record (before the reference year) and the current claims are a good predictor of future claims, provided the requirements of the class of risk (or case pricing) of the insured. It is assumed, depending on the accident record, that each class of risk has two categories of drivers insured: low-risk and high-risk. Using a negative binominal distribution and a Bayesian approach, we show that the probability of being a low risk driver is more important in the absence of losses (or with a single claim) and that conversely the probability of an insured high risk greatly increases when the insured has 2 or 3 losses during the reference year. Of course the level of probability varies according to risk classes. In all cases, the previous accidents are a good indicator of future claims.