1.

In how many ways can the data in Table 9.1 be organized in a table, by year of origin, year of development and calendar year, vertically or horizontally, in increasing or decreasing order?

1.

24.

1.

Show that (9.6) and (9.7) indeed produce the same estimate.

2.

Prove (9.10). What is the mode of the random variables X _ij in model (9.9)?

3.

Apply the chain ladder method to the given IBNR triangle with cumulated figures. What could be the reason why run-off triangles to be processed through the chain ladder method are usually given in a cumulated form?

4.

Apply the arithmetic separation method to the same data of the previous exercise. Determine the missing ? values by linear or by loglinear interpolation, whichever seems more appropriate.

5.

Which distance between data and predicted values is minimized by the chain ladder method? Which by the separation methods?

1.

2.

The mode of the lognormal( ?, ? ²) distribution is , see Exercise 3.8.6.

3.

4.

5.

See the previous chapter.

1.

Verify that the same predictions (9.12) are obtained from the models E[ X _ij] = ? ? _i ? ^{j -1}