Actuarial Notes

CAS Exam 8 Fall 2013, Question 15

Study guide: Exam 8

The following diagram depicts a book of business for a retrospectively rated workers compensation plan:

The descriptions of the labels on the diagram are as follows:

  • r_1 = Aggregate minimum.
  • r_2 = Aggregate maximum.
  • Total loss - Total aggregate losses with no per-accident limit.
  • Limited loss - Total aggregate losses after application of a per-accident limit.

Part a (1.5 points)

Using the letter labels above to represent portions of the graph, describe the following quantities:

  1. \phi - The Table M insurance charge at r_2.
  2. \psi - The Table M savings at r_1.
  3. \phi^* - The Table L insurance charge at r_2.
  4. \psi^* - The Table L savings at r_1.
  5. I - The amount expected to be paid by the insured with an aggregate limit but no per-accident limit.
  6. I* - The amount expected to be paid by the insured in the presence of both an aggregate and a per-accident limit.

Part b (0.75 points)

A change in relevant workers compensation law goes into effect that causes a significant increase in the most severe losses. Briefly explain what effect this is likely to have on the areas of E and H in the above diagram.

Part c (1 point)

Assume loss frequency and severity are independent, all individual losses come from the same distribution, and the only difference between large and small accounts is the number of expected claim counts. Determine whether the above diagram is accurate for both large and small accounts. Justify your answer.

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Concepts tested

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