SOA Exam ASTAM Spring 2026, Question 5

Study guide: Exam ASTAM

You are analyzing the following cumulative claims run-off triangle for a commercial insurance. Assume that claims are fully developed by the end of Development Year 2.

Accident Year (AY) $i$ / Development Year $j$	0	1	2
0	235	317	349
1	320	390
2	416

Part a (2 points)

You first use the chain ladder method to estimate the ultimate claims.

(i) Show that the projected cumulative claims for AY1 are 430 to the nearest 10. You should calculate the value to the nearest 1.

(ii) Calculate the projected cumulative claims for AY2.

Part b (1 point)

You next decide to estimate the outstanding claims using the Bühlmann-Straub model. You are given that $\hat{\gamma}_0 = 0.71303$ , $\hat{\gamma}_1 = 0.19528$ , and $\hat{\gamma}_2 = 0.09169$ .

Explain in words what the $\gamma_j$ values represent.

Part c (3 points)

You are given that $s_0^2 = 625.41$ and $\bar{C} = 440.61$ .

Show that $\hat{v}$ is 940 to the nearest 10. You should calculate the value to the nearest 0.1.

Part d (3 points)

You are given that $\hat{a} = 12{,}231$

(i) Calculate the credibility factors, $Z_0$ , $Z_1$ , $Z_2$ .

(ii) Explain briefly why, in general, we expect $Z_0 > Z_1 > Z_2$ .

(iii) Show that $\hat{\mu} = 452.77$ .

(iv) Calculate the Bühlmann-Straub estimate of the projected cumulative claims for AY 2.

Part e (2 points)

The Bornhuetter-Ferguson method can also be expressed as a credibility estimate. Describe two advantages and one disadvantage of the Bühlmann-Straub approach compared with the Bornhuetter-Ferguson method. You do not need to describe the Bornhuetter-Ferguson method in detail.

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