Free CAS Exam 5 (Basic Ratemaking and Reserving) Unpaid Claim Estimation Techniques Practice Questions

Practice 87 free Unpaid Claim Estimation Techniques questions for CAS Exam 5 (Basic Ratemaking and Reserving).

87 Questions

24 Easy

32 Medium

31 Hard

2026 Syllabus

Sample Questions

Question 1 Easy

In the Bornhuetter-Ferguson (BF) method, how are estimated unpaid claims computed?

Solution

A is correct. The Bornhuetter-Ferguson method estimates unpaid claims as expected (a priori) claims multiplied by the percentage of claims still unreported,

1 - 1/ CDF

. This blends an a priori expected-claims estimate with the development pattern, giving stability when reported data are thin.

Question 2 Medium

For accident year 2024, cumulative reported (incurred) losses at 24 months are 6,000 (in thousands). The actuary selects a cumulative development factor to ultimate of 1.25. Paid losses to date are 4,200 (in thousands). What is the estimated IBNR?

Solution

A is correct. Ultimate losses equal reported losses developed to ultimate:

6, 000 \times 1.25 = 7, 500.

IBNR is the amount not yet reported, i.e., ultimate less reported (incurred) losses:

7, 500 - 6, 000 = 1, 500 (thousands) .

(Case reserves of

6, 000 - 4, 200 = 1, 800

are already reported and are not part of IBNR.)

Question 3 Hard

An accident year has earned premium of 20,000, an a priori expected loss ratio of 60%, a reported-to-ultimate cumulative development factor (CDF) of 2.00, and reported losses to date of 5,000. Using the Gunnar Benktander method, what is the estimated ultimate loss (in dollars)?

Solution

B is correct. Expected losses =

20, 000 \times 0.60 = 12, 000

. The percent reported =

\frac{1}{2.00} = 0.50

, so the unreported percent is

0.50

. The Bornhuetter-Ferguson ultimate = reported + unreported × expected =

5, 000 + 0.50 \times 12, 000 = 11, 000.

The Benktander method uses the BF ultimate as the new a priori: GB ultimate = reported + unreported × (BF ultimate) =

5, 000 + 0.50 \times 11, 000 = 10, 500.

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