Bootstrapping the ODP / CL

[Ash_B]

Hi

In section 5.7 of Chapter 14 (Bootstrapping the ODP - relating the theory to the practise), it says that in a special case of the ODP model, the expected values are the same as the basic chain ladder, but it doesn't say what the special case is.

Is this referring to a specific GLM that achieves this? Maximum likelihood on the development factors?

Thanks
Ash

 

[MorningtonCrescent]

It's referring to a specific GLM, ie the specific linear predictor and specific parameters of the ODP distribution.

Check out this link: http://www.actuaries.org.uk/researc...tive-distributions-outstanding-liabilities-un

 

[zuglubuglu]

Fitting Values

With reference to step 1 on page 20, am I right in assuming that the fitted values lead to zero residuals in the anti-diagonal?

That is rather than predicting cumulative claims paid to date assuming that the claims paid in the first year of development are correct, we estimate the cumulative claims paid during the years of development assuming the cumulative claims paid to date are correct.

(Same argument applies for claims incurred)

 

[Darren Michaels]

Hi there

The residuals on the last diagonal are not zero because the residuals are based on incremental rather than cumulative claims data.

As you correctly state the method assumes that the cumulative claims to date (ie the leading or latest diagonal)are correct and then "back fills" the past data using the chain ladder development pattern, starting from the latest diagonal.

The residuals are then calculated as the difference between the actual and estimated incremental claims data.

This means the last diagonal of residuals is unlikely to be zero as the expected penultimate diagonal of the cumulative triangle is unlikely to be equal to the actual penultimate diagonal.