Imprecise credibility theory

The classical credibility theory is a cornerstone of experience rating, especially in the field of property and casualty insurance. An obstacle to putting the credibility theory into practice is the conversion of available prior information into a precise choice of crucial hyperparameters. In most real-world applications, the information necessary to justify a precise choice is lacking, so we propose an imprecise credibility estimator that honestly acknowledges the imprecision in the hyperparameter specification. This results in an interval estimator that is doubly robust in the sense that it retains the credibility estimator’s freedom from model specification and fast asymptotic concentration, while simultaneously being insensitive to prior hyperparameter specification.

Individual Loss Reserving Using a Gradient Boosting-Based Approach

In this paper, we propose models for non-life loss reserving combining traditionalapproaches such as Mack’s or generalized linear models and gradient boosting algorithm in anindividual framework. These claim-level models use information about each of the payments madefor each of the claims in the portfolio, as well as characteristics of the insured. We provide an examplebased on a detailed dataset from a property and casualty insurance company. We contrast sometraditional aggregate techniques, at the portfolio-level, with our individual-level approach and wediscuss some points related to practical applications.