ASMF seminar: Olivier Lopez (Université Pierre et Marie Curie Paris VI)
'Prediction of the Amount of a Claim Using a Copula Model in Micro-Level Reserving'
We present a new methodology to improve the evaluation of RBNS claims (Reported But Not Settled) in non-life insurance claim reserving. The methodology combines survival analysis tools and copula analysis to forecast the final amount of a claim, based on a potentially large number of known characteristics. The copula model allows to capture the dependence between the "lifetime" of the claim (time before its settlement) and its cost, and is particularly adapted to guarantees with potential long lifetime of the claims. A model selection of the copula family is proposed, based on an empirical analysis. The prediction of the final amount of the claims is also associated with an evaluation of the uncertainty behind this prediction, which can be done using an asymptotic approach based on our investigation of the theoretical behavior, but also by a bootstrap procedure. Beyond the theoretical validity of the procedure, we illustrate the behavior of the procedure through a simulation study and a real data analysis coming from medical malpractice claims. An extension to the evaluation of IBNR claims (Incurred But Not Reported) is also proposed, making this procedure a valuable tool in a micro-level reserving approach, or in improving experts diagnosis in evaluating the claims.
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