Modeling the occurrence of events subject to a reporting delay via an EM algorithm

Abstract

A delay between the occurrence and the reporting of events often has practical implications such as for the amount of capital to hold for insurance companies, or for taking preventive actions in case of infectious diseases. The accurate estimation of the number of incurred but not (yet) reported events forms an essential part of properly dealing with this phenomenon. We review the current practice for analysing such data and we present a flexible regression framework to jointly estimate the occurrence and reporting of events from data at daily level. By linking this setting to an incomplete data problem, estimation is performed by the expectation-maximization algorithm. The resulting method is elegant, easy to understand and implement, and provides refined forecasts on a daily level. The proposed methodology is applied to a European general liability portfolio in insurance.