Accurate estimation of value-at-risk (VaR) and assessment of associated uncertainty is crucial for both insurers and regulators, particularly in Europe. Existing approaches link data and VaR indirectly by first linking data to the parameter of a probability model, and then expressing VaR as a...

In the context of predicting future claims, a fully Bayesian analysis --- one that specifies a statistical model, prior distribution, and updates using Bayes's formula --- is often viewed as the gold-standard, while Buhlmann's credibility estimator serves as a simple approximation. But those...