Schwankung der Abwicklungsergebnisse

In the Sandbox-Version, in the register "Chain-Ladder", there is a button "Schwankung der Abwicklungsergebnisse". Concerning this, I have some questions to the developers of this wonderful new application.

What is the formula behind the calculated values of "Abwicklungsergebnis (1 Periode) Standardabweichung" (Question 1)?

I suppose, that there is a link to the paper http://www.math.ethz.ch/~wueth/Papers/CDR_WuMeLy.pdf

Using the triangle given in this paper, the values of "Abwicklungsergebnis (1 Periode) Standardabweichung" are nearly the same as the column VarHat^(1/2) in table 6!

But there is a difference in the oldest estimated standard deviation. Wüthrich/Merz/Lysenko use as estimator of the sigma of the last Chain-Ladder-Development the "standard value" from Mack (1993), sometimes labelled as geometric rule. What estimate is used in the sandbox (Question 2)? Is there a choice/option to change this estimate (Question 3)?

And finally (Question 4), do you plan to program more of the calculations of Wüthrich/Merz/Lysenko into the Reserving Application?

Thanks for the flowers ... and the pertinent questions.

Here are some elements of response:

1. Yes http://www.math.ethz.ch/~wueth/Papers/CDR_WuMeLy.pdf   is is the paper our code is based upon.
   
2. I also get small differences when trying to recalculate Mack's standard error for the 2 oldest years. 
   
3. Currently, the rule is hard wired because currently the interface allowing to set  "User preferences" and store them is not yet available. But it's on our agenda.
   
4. We plan to apply the calculation backward, i.e. to the triangle without the last diagonal and then compare the estimates for the deviation with observed development. 
   If you have other ideas, and it seems to me you do, feel free to make suggestions here.
   

I hope this helps

The differences probably come from the fact that the original data were not

rounded numbers, i.e. they had decimal places.

Since the Wüthrich/Merz/Lysenko paper that will soon appear in the Scandinavian

Actuarial Journal (SAJ) has attracted quite some attention, we have written a

conference paper on the same subject for ASTIN 2008. The conference paper

gives linear approximations to the SAJ results which simplifies the formulas.

Moreover, we have added remarks that should now explain the results more

clearly. The conference paper can be downloaded from

Thanks to Mario Wüthrich for providing the data with full decimals.

We corrected some bugs and have updated the sandbox and the installer version.

The results of the paper can now accurately be reproduced.

Here is a quick "how-to":

   1. Choose any node in the LoB tree
   2. Above the tabs set Data format to "cumulative"
   3. In the properties tab, set number of reporting periods to 9 years (->"accept")
   4. Drag and drop the data below into the "Loss and Premium" tab
   5. Select the ChainLadder tab, press "Runoff result standard deviation"

 

Thanks Stefan,

The link is not working. Kindly send us the new link of paper (CDR_WuMeLy.pdf).

Regards,

Srini.

Previously Stefan Zumsteg wrote:

Thanks for the flowers ... and the pertinent questions.

Here are some elements of response:

1. Yes http://www.math.ethz.ch/~wueth/Papers/CDR_WuMeLy.pdf   is is the paper our code is based upon.
   
2. I also get small differences when trying to recalculate Mack's standard error for the 2 oldest years. 
   
3. Currently, the rule is hard wired because currently the interface allowing to set  "User preferences" and store them is not yet available. But it's on our agenda.
   
4. We plan to apply the calculation backward, i.e. to the triangle without the last diagonal and then compare the estimates for the deviation with observed development. 
   If you have other ideas, and it seems to me you do, feel free to make suggestions here.
   

 

I hope this helps

 

 

 

Mario Wüthrich has restructured his webpage. The mentioned paper is no longer available under this link. Have a look at http://www.math.ethz.ch/~wueth/talks2.html. Maybe you can find something similar.