2012 Fall Q19
What are the "retrospective development factor" and corresponding "retrospective development premium"? I didn't see these topics in the wiki.
What are the "retrospective development factor" and corresponding "retrospective development premium"? I didn't see these topics in the wiki.
Comments
This is an older question which, while still relevant today, contains terms that previously may have been discussed in greater detail. Today, the CAS would expect you to infer what these mean.
A brief discussion of retrospective development is at the bottom of the following wiki article.
https://battleacts8.ca/8/wiki/index.php?title=NCCI.Circular
Basically, an insured has two options - use retrospective development or not. The retrospective loss development factors produce an estimate of the ultimate retrospective loss at early maturities so we avoid the situation of large premium refunds because early experience has come in favorable, only to then later request large additional premiums because the losses were finally reported/adjusted. Retrospective development for premiums stabilizes the early retrospective premiums charged to avoid this situation.
For this problem, why do you use Standard Premium and not Expected Loss?
I think you're referring to why do we multiply the retrospective development factor by the standard premium instead of the actual loss to date - please let me know if this isn't what you're thinking.
The Fisher text only mentions retrospective development in passing. This question predates the Fisher text so the topic was likely discussed in more detail. There is a footnote on page 26 of the source which says for the ISO and NCCI retrospective rating plans the retrospective development factors are expressed as a percent of standard premium.
The other clue that the retrospective development factor is a percent of standard premium is we typically express the basic premium B as a percent of standard premium, so we want to keep the denominator consistent across all the terms in the retro premium equation.
Model solution 1 works with dollars which makes it easier to follow in our opinion. In this solution, we have to recall that the excess loss factor is not k but is actually (E[A] - E{A_D])/(Standard Premium). See the comment here for a note along these lines:
https://battleacts8.ca/8/wiki/index.php?title=Fisher.TableL#The_Insurance_Charge_Reflecting_Loss_Limitation_(ICRLL)_Method
That answers my question. Thanks! I was not making the distinction between k and the excess loss factor.