Mack’s Estimator Motivated by Large Exposure Asymptotics in a Compound Poisson

The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, that is of compound Poisson type, are not consistent with Mack’s distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g., number of contracts), we show that the chain ladder predictor and Mack’s estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack’s estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.

Filip Lindskog obtained a PhD in mathematics at the Swiss Federal Institute of Technology (ETHZ) and is currently Professor of Insurance Mathematics at Stockholm University. He is head of the division Mathematical Statistics at Stockholm University, director of the Master’s Program in Actuarial Mathematics, and an editor of Scandinavian Actuarial Journal.

Norbert Haible is a seasoned professional from Luxembourg, boasts a wealth of experience and expertise in the realm of reinsurance He has navigated diverse roles, including Reinsurance Underwriter and Head of Technical Management & Claims at KBC Group Re. His astute insights and proficiency extend across key domains such as reinsurance structuring, pricing, and reserving, alongside adept risk modeling and adherence to regulatory frameworks like Solvency II. Currently serving as a Member of the ASTIN Board, with a tenure extending to 2027, Norbert exemplifies dedication to advancing industry standards while maintaining an unwavering commitment to data management excellence.