Description: Actuarial concepts of credibility can be extended to encompass additional information provided by new machine learning estimates. New statistical ideas also indicate how to generalize to blend arbitrarily many estimators, while not double-counting common information. For example, historical claim costs and risk scores both leverage diagnosis code information. We introduce two new estimators, one based on partial correlation and the other based on the machine learning-derived Shapley statistic, to address these limitations.

Description: Uncertainty of a predictive model is a fact of life that many insurers could be overlooking at their peril without a framework for assessing it. The article provides a framework to understand the prediction uncertainty, which can be critical for the insurance operations using predictive models. Coin toss example explains model uncertainty and randomness inherent in making predictions to the number of heads expected. A mortality analysis case study illustrates how the Bayesian methodology can be used to develop the prediction uncertainty. In particular, the article shows that the Bayesian framework is a way to combine historical data and actuarial judgment, and directly address the model uncertainty through its posterior distribution.

Description: A significant fraction of insurance risk is characterized by the tail of the claims distribution, where we have much less data to model probabilities accurately. Ignoring the tails can lead to underpricing of tail risk and mispricing. Estimation of the tails can be complex due to a bias-variance tradeoff--the further out we go into the tail the more accurately we can model the extreme tail (lower bias) but the less data we have (increased variance). The statistical tools of Extreme Value Theory can be leveraged to more accurately estimate both the incidence and the severity of extreme events given that they occur. using the Generalized Pareto Distribution.

Description: An introduction to the methods and parameters for Bayesian Hyperparameter Optimization in a Life Insurance context.