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Title: A micro-level study of IBNR claims reporting delays using extreme value theory Authors:  Maud Thomas - Sorbonne University (France) [presenting]
Jonathan El Methni - Universite Paris Descartes (France)
Abstract: The evaluation of the volume of IBNR claims (Incurred But Not Reported) is a challenging task in claim reserving. A standard way to proceed is to rely on chain-ladder type techniques. These techniques are based on an aggregate vision of the risk, and on a stability of the payment process. The prediction obtained via chain-ladder usually does not distinguish between IBNR and RBNS claims (Reported But Not Settled). Recently, interest in looking more precisely in the reporting dynamic has increased. We propose a method to perform a closer look of IBNR by studying the distribution of a large delay before reporting a claim at a micro-level using Extreme Value Theory. The distribution of largest IBNR claims reporting delays belongs to the family of Weibull-tail distributions. Such distributions have already been used to model large claims in non-life insurance. The behaviour of these distributions is characterised by a shape parameter, called the Weibull-tail coefficient. We derive a data-driven procedure to estimate this coefficient using techniques inspired by Lepski's method.