Closed-Form Distribution of Prediction Uncertainty in Chain Ladder Reserving by Bayesian Approach

Bayesian approach is applied to evaluate the prediction uncertainty in chain ladder reserving. First, the philosophy of the Bayesian approach to prediction uncertainty is introduced and compared with the Frequentist approach. All parameters in the model are then estimated using the Bayesian approach, with multiple types of prior distributions. A closed-from posterior distribution is derived under noninformative and conjugate prior distribution for key parameters in the model. Finally, the theory is illustrated by numerical examples. The paper demonstrates that it is possible to derive closed-form estimates for the prediction uncertainty in chain ladder reserving using the Bayesian approach and that, for certain prior distributions, the estimated uncertainty could be much higher than estimates of uncertainty produced under the Frequentist approach.

Keywords: Bayesian approach; Prediction uncertainty; Chain ladder; Reserving; Student t distribution; Inverse Gamma distribution.