Collective Risk Modelfor Paid Loss Collective Risk Model for Paid Loss Development

Stochastic models for claim payment triangles usually suffer from the defect that they hold no description for the discrete probability of no payments in any given cell. To remedy this defect, we have investigated a Poisson-exponential collective risk model – notable for its mathematical convenience – with parametric forms for mean paid claim count and mean paid claim size in each accident-year/payment-year cell. We present expressions for the likelihood function, and forecast mean and variance. We then discuss fitting diagnostics since the model does not have residuals in the usual sense. Finally, we present and discuss the results of several case studies.