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

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.