SOA PAPredictive Analytics

A model's training RMSE is 120 and test RMSE is 210; a simpler model has training RMSE 150 and test RMSE 160. Which should be recommended and why?

For predicting claim severity that is strictly positive and right-skewed, the most appropriate GLM specification is:

You are asked to predict whether a workers' compensation claim will exceed 100,000. The dataset includes 'total paid to date'. Explain whether to use this field and propose two legitimate alternatives.

A survey field is missing more often for young respondents than old respondents, but within each age group missingness is unrelated to the survey answer itself. This missingness mechanism is best described as:

Two predictors in a pricing dataset, vehicle age and vehicle value, have a correlation of 0.85. Explain the practical consequences of including both in a GLM without treatment, and propose two remedies.

Compared with ridge regression, lasso regression:

You suspect the effect of driver age on claim frequency differs by vehicle class (sports car vs sedan). Describe how you would test and, if warranted, incorporate this in a GLM, and how you would guard against overfitting.

Explain how k-fold cross-validation is used to select the lasso penalty parameter $\lambda$, and why choosing $\lambda$ to minimize training error would be inappropriate.

A binary classifier assigns scores 0.9, 0.8, 0.4 to the three actual positives and 0.7, 0.3, 0.2 to the three actual negatives in a test set. Calculate the AUC using the rank/concordance interpretation.

Draft the key points of an executive summary explaining to a non-technical Chief Underwriting Officer why you recommend a gradient-boosted tree model over a GLM for a new pricing model, including its limitations.