Accurate prediction of future claims is a fundamentally important problem in insurance. The Bayesian approach is natural in this context, as it provides a complete predictive distribution for future claims. The classical credibility theory provides a simple approximation to the mean of that...

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...

Over the last two decades, Bayesian methods have been widely used in general insurance applications, ranging from credibility theory to loss-reserves estimation, but this literature rarely addresses questions about the method's asymptotic properties. In this paper, we review the Bayesian's...

Insurance regulation often dictates that insurers monitor their solvency risk in real time and take appropriate actions whenever the risk exceeds their tolerance level. Bayesian methods are appealing for prediction problems thanks to their ability to naturally incorporate both sample variability...

The foundation of insurance in the frequentist framework is well-understood by experts in actuarial science, insurance and risk management. In the past two decades there has been a surge in the application of Bayesian analysis in insurance. However, the foundation of insurance under the Bayesian...