Chapter 15 bootstrapping the ODP

[Jayant]

Hi.
On page 19 of chapter 15, there is a link to discussions on bootstrapping which includes a worked example. The link given is http://tinyurl.com/p4gu5op . I've tried the link but it takes me to a German actuarial site and from what I can make out, it says the site was not found or does not exist. Can someone please direct me to the correct discussion site?

Alternatively, if you could elaborate on step 2 of the bootstrapping process on page 20 of chapter 15, that would help. I get that you need to sample from the residuals with replacement, but I don't quite understand how you get alternative past data sets. Do you take the fitted values and add the sampled residuals? And then how do you get a full triangle of residuals if you are only taking a sample?

 

[Hemant Rupani]

Alternatively, if you could elaborate on step 2 of the bootstrapping process on page 20 of chapter 15, that would help. I get that you need to sample from the residuals with replacement, but I don't quite understand how you get alternative past data sets. Do you take the fitted values and add the sampled residuals? And then how do you get a full triangle of residuals if you are only taking a sample?

Here, section 5.4 is applicable and there the process is explained in ActEd wordings.

 

[Darren Michaels]

Hi Jayant

Unfortunately the paper that we were referring to has been removed from the Swiss Actuarial Association's website. I have tried to search for it but unfortunately I can't seem to find it anywhere else. However, there are plenty of other papers available on the IFoA website which discuss bootstrapping if you are looking for some background reading here.

To clarify how Step 2 works, you sample a residual (with replacement) for each different cell in your data triangle and then for each cell you add the sampled residual onto the fitted value for that cell that you calculated in Step 1. This produces a "pseudo" data triangle, which you can then project to ultimate using the basic chain ladder method (Step 3). You then repeat Steps 2 and 3 many times to get a distribution for the ultimate claims amount.

As mentioned on page 21 of Chapter 15 you can apply this process with varying degrees of sophistication surrounding the sampling of residuals. In its simplest form you can allow any residual to be sampled for any cell in the triangle, but more complicated variations exist where you restrict which residuals can be sampled for which cells in the triangle.