SOA Exam ASTAM Sample Question 20

Study guide: Exam ASTAM

You are given the following run-off triangle of incremental claim payments, $X_{ij}$ . Assume all claims are settled by the end of development year 4.

Accident Year (AY) $i$	DY $j$ = 0	1	2	3	4
0	1023	132	188	43	10
1	1358	350	197	25
2	1283	283	172
3	1503	508
4	1536
$\hat{\beta}_j$	0.6931	?	0.9725	0.9928	1.000
$\hat{\gamma}_j$	0.6931	?	0.1086	0.0204	0.0072

Part a

(i) Show that $\hat{\beta}_1 = 0.86$ to the nearest 0.01. You should calculate the value to the nearest 0.001.

(ii) Show that $\hat{\gamma}_1 = 0.17$ to the nearest 0.01. You should calculate the value to the nearest 0.001.

Part b

Calculate the estimated outstanding claims using the chain ladder method.

Part c

Write down the three assumptions of the Bühlmann-Straub model of outstanding claims.

Part d

Using the Bühlmann-Straub model,

(i) Calculate $s_2^2$ .

(ii) You are given that $\hat{v} = 30{,}582$ . Calculate $\hat{a}$ .

(iii) Describe briefly what $\hat{v}$ and $\hat{a}$ are measuring.

(iv) You are given that $\hat{\mu} = 1926.2$ . Calculate $\hat{C}_{2,4}^{BS2}$ .

Part e

Explain briefly how the Bühlmann-Straub model can be seen as a special case of the Bornhuetter-Ferguson model.

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