SOA Exam ASTAM Fall 2025, Question 5

Study guide: Exam ASTAM

A casualty insurance company sells a product that pays a single fixed payment of 200 if the insured is hospitalized.

The following are the cumulative claim payments, in 000's, from the third quarter of 2023 through to the end of 2024.

You can assume that there are no claim payments after Development Quarter 5.

Cumulative claim payments by quarter-year (in 000's)

Part a (4 points)

(i) Show that the projected cumulative claims incurred in 2024, using the Chain Ladder method, total 1840 to the nearest 10. You should calculate your answer to the nearest 0.1.

(ii) Explain why the inflation-adjusted chain ladder would not be appropriate in this case.

(iii) Calculate the projected claims payments in Quarter 2 of 2025 in respect of claims arising in 2024.

Part b (1 point)

Explain what is meant by the term "calendar year effect" in relation to estimating outstanding claims using the chain ladder method.

Part c (4 points)

The insurer uses the 'Large (L) – Small (S)' test of development factors to test for calendar year effects by quarter-year. The L-S triangle for the development factors is given below. Median values are indicated by *.

Let k = 1 denote the quarter year Q4-2023, k = 2 denote the quarter year Q1-2024, etc.

(i) Write down the null hypothesis for the test.

(ii) Write down the values of n_k, m_k, and Z_k for k = 1, 2, 3, 4.

(iii) Calculate E[Z_4] under the null hypothesis.

(iv) You are given that under the null hypothesis, E[Z] = 3.0 and \text{Var}[Z] = 1.125. Calculate the p-value of the test.

(v) State the conclusion of the test.

Part d (1 point)

Describe one reason why there might be a calendar year effect in a claims development triangle.

Answer this question and see the worked solution

Concepts tested

• Chain Ladder Method
• Calendar Year Effect
• Chain Ladder Assumptions
• Development Factor
• Inflation
• Unpaid Claims

More questions from this set

• SOA Exam ASTAM Fall 2025, Question 4
• SOA Exam ASTAM Fall 2025, Question 6