A new perspective from a Dirichlet model for forecasting outstanding liabilities of nonlife insurers

TL;DR

This paper introduces a Dirichlet model that unifies Chain-Ladder and Bornhuetter-Ferguson methods for forecasting nonlife insurance liabilities, offering a flexible statistical framework with both frequentist and Bayesian inference.

Contribution

The paper proposes a novel Dirichlet model that provides a unified framework for two major actuarial approaches, enabling more consistent and informed reserve predictions.

Findings

The Dirichlet model can replicate Chain-Ladder and Bornhuetter-Ferguson predictions.

The model supports both frequentist and Bayesian inference methods.

Application to US workers' compensation data demonstrates its practical utility.

Abstract

Forecasting the outstanding claim liabilities to set adequate reserves is critical for a nonlife insurer's solvency. Chain-Ladder and Bornhuetter-Ferguson are two prominent actuarial approaches used for this task. The selection between the two approaches is often ad hoc due to different underlying assumptions. We introduce a Dirichlet model that provides a common statistical framework for the two approaches, with some appealing properties. Depending on the type of information available, the model inference naturally leads to either Chain-Ladder or Bornhuetter-Ferguson prediction. Using claims data on Worker's compensation insurance from several US insurers, we discuss both frequentist and Bayesian inference.