CAS Exam 8Advanced Ratemaking

Expected losses per policy limited to the 100,000 basic limit are 500. Expected losses limited to 1,000,000 are 800. Ignoring ALAE and risk load, calculate the increased limits factor for 1,000,000.

A risk has expected losses of 200,000 and actual losses of 250,000 over the experience period. The credibility constant is $K=50{,}000$. Using $M=1+Z(A/E-1)$ with $Z=E/(E+K)$, calculate the experience modification.

A retrospective rating plan has basic premium 20,000, loss conversion factor 1.10, tax multiplier 1.04, minimum premium 40,000 and maximum premium 120,000. Incurred losses are 60,000. Calculate the retrospective premium.

The ground-up pure premium is 1,000 and the loss elimination ratio at a 500 deductible is 15%. Calculate the pure premium net of the deductible.

When fitting a Poisson frequency GLM with a log link to policies of varying exposure, the recommended treatment of exposure is to:

Contrast the Bailey minimum-bias procedure with a multiplicative GLM for classification ratemaking. Explain (a) how each derives relativities, (b) why certain GLMs reproduce minimum-bias results exactly, and (c) three advantages of the GLM framework.

A catastrophe excess-of-loss treaty covers the layer 5,000,000 excess of 5,000,000 (i.e., limit 5,000,000). The modeled average annual loss to the layer is 1,000,000. Calculate the rate on line.

Which statement best distinguishes exposure rating from experience rating in reinsurance pricing?

ILFs are 1.00 at 100,000, 1.35 at 250,000, and 1.55 at 500,000 (basic limits premium normalized to 1.00 at the 100,000 limit). Calculate the marginal increased limits factors for the 100k-250k layer and the 250k-500k layer, and state whether the consistency (diminishing marginal layer cost) test is satisfied.

A retrospective rating plan has basic premium 15,000, loss conversion factor 1.05, tax multiplier 1.00, minimum premium 30,000 and maximum premium 150,000. Losses limited by the per-occurrence limitation total 70,000. Calculate the retrospective premium.

A Tweedie GLM with a log link is fit to pure premium directly (rather than fitting separate frequency and severity GLMs). (a) State the key structural assumption linking the Tweedie power parameter $p$ to a compound Poisson-gamma process. (b) Give one advantage of the single-Tweedie-model approach over separate frequency/severity models. (c) Give one advantage of the separate-model approach over the single Tweedie model.