Apply custom cumulative factor to the latest diagonal (Chain Ladder Example from Wikipedia)

[alexbcz]

Hi Everyone,

I'm trying to reproduce the example showed on the wikipedia page about Chain Ladder : https://en.wikipedia.org/wiki/Chain-ladder_method#Example

I could reproduce all the calculations showed on the page, but I'm still missing the last table : Estimation of ultimate claims

I know how to get the cdf I want to apply:
cl.Development(average="volume", n_periods=3).fit(xyz_tri["Incurred"]).cdf_

I know how to get the latest diagnoal:
xyz_tri.latest_diagonal

But how to apply the cdf to the latest diagonal in order to get the latest table of the example?
I think, I'm also missing how to calculate the tail factor?
Another question: Can I apply the cdf to the whole triangle to get the full triangle based on these cdf?

Here's what I have done so far : https://github.com/alexbcz/wikipedia_chain_ladder_example/blob/main/Wikipedia%20ChainLadder%20example.ipynb

Thank in advance

[jbogaardt]

Sounds like you want the multiplicative Chainladder estimator. I would refer you to @kennethshsu's excellent tutorial on the subject.

[alexbcz]

Thanks a lot John,
It worked perfectly.
If there are folks willing to do the same, I updated the notebook with the solution provided : https://github.com/alexbcz/wikipedia_chain_ladder_example/blob/main/Wikipedia%20ChainLadder%20example.ipynb

I have an other question, once I did the job with the reported claims, I wanted to do the same with the paid claims.
The full example is not on Wikipedia, I found it on the casact website : https://www.casact.org/sites/default/files/database/studynotes_friedland_estimating.pdf
Whereas with the reported claims no tail factor was applied, for the paid claims they applied a tail factor of 1.002
As no specific tailing method is mentionned in the document, I used cl.TailConstant(1.002)
I got almost the same results than the document for the utimate paid claims (less than 0.05% of difference in the worst case).
But I am bit confused, because when I look at the ldfs of my model, I can't see my custom tail factor :

	12-24	24-36	36-48	48-60	60-72	72-84	84-96	96-108	108-120	120-132	132-144
(All)	1.702	1.186	1.091	1.044	1.019	1.009	1.005	1.002	1.002	1.001	1.001

Am I missing something?

[hoverat]

Did you look at your cdfs?

[alexbcz]

Here is what I got for the cdfs:
12-Ult 24-Ult 36-Ult 48-Ult 60-Ult 72-Ult 84-Ult 96-Ult 108-Ult 120-Ult 132-Ult
(All) 2.391 1.404 1.184 1.085 1.040 1.021 1.011 1.006 1.004 1.002 1.001

Here we can see the tail factor of 1.002
So everything looks good 👍
Thank you and sorry for the confusion 😅