This presentation will illustrate how Bayesian Monte-Carlo Markov Chain (MCMC) methods can be used to construct Stochastic Loss Reserve Models that predict the distribution of (1) ultimate losses, and (2) calendar year losses.  The presentation will then test the distributions predicted by these models, and other standard models such as Mack and ODP/Bootstrap, with outcome data that is in the CAS Loss Reserve Database.  

I expect the results obtained to date to generate some interesting discussions.  There are

1. When applied to cumulative incurred data, the Mack model understates the variability of the outcomes.
2. The Correlated Chain Ladder (CCL) model, applied to cumulative incurred claims data, can predict the distribution of outcomes within a 95% confidence range based on separate analyses of 200 loss triangles.
3. When applied to incremental paid losses, the ODP/Bootstrap gives a biased prediction of the distribution of outcomes.
4. The Correlated Incremental Trend (CIT) model is an attempt to fix that problem by introducing a payment year trend.  Its predictive distribution is similar to that of the ODP/Bootstrap model and it fails to fix the problem.

One conclusion that can be drawn for this is that there is information that claims adjusters use in setting their loss reserves, that is not observable in the paid claims data.  These conclusions are debatable and need discussion.