CAS Exam 7 Spring 2013, Question 9

Study guide: Exam 7

An actuary is considering a Bayesian approach to developing a predictive loss distribution based on the deterministic chain-ladder method using the all-years weighted average link ratios.

Part a (0.5 points)

To produce results that closely resemble the deterministic chain-ladder outcome, explain whether the actuary should select high or low variances for the prior distributions of the link ratios.

Part b (0.5 points)

The actuary decides to override the link ratios suggested by the data for the 36-48 month maturity interval with a judgmental selection. However, the actuary is less confident of this selection than of the all-years weighted averages used for the other maturity intervals. Describe how to change the prior distributions of the link ratios to adjust for this.

Part c (1 point)

Discuss the effect of the change implemented in part b. above on the simulated results, addressing both the mean and the prediction error.

Part d (1 point)

Describe one advantage that a Bayesian approach has over a bootstrapping algorithm and one advantage that a Bayesian approach has over the Mack method.

Part e (0.5 points)

Discuss a modification to the Bayesian framework for the chain-ladder method so that it applies to the Bornhuetter-Ferguson method.

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