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

TL;DR

This paper introduces a flexible EM-based regression framework to accurately estimate the occurrence of events with reporting delays, aiding in better decision-making in insurance and public health.

Contribution

It presents a novel EM algorithm approach for jointly modeling event occurrence and reporting delays, improving estimation accuracy over existing methods.

Findings

Effective in estimating unreported events in insurance data

Provides refined nowcast insights

Applicable to real-world insurance portfolio data

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. By linking this setting to an incomplete data problem, estimation is performed via an expectation-maximization algorithm. The resulting method is elegant, easy to understand and implement, and provides refined insights in the nowcasts. The proposed methodology is applied to a European general liability portfolio in insurance.