Stochastic loss reserving: A new perspective from a Dirichlet model

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 U.S. insurers, we discuss both frequentist and Bayesian inference.