Is it possible to construct a triangle that has less development year than the actual data ? in other words, one would assume that the claim will settled for k period while for claim in k+1 until n period will be adjust into k period. Is this considered fraud or merely an actuarial judgement ?
Can one construct a run-off triangle with loss - submit date with approved claim amount ? or should one use loss - paid date using with claim amount or loss - submit date with submit amount ?
So your actual data has development for 60 months but you construct a triangle that ends at 48 months? Sure you can do that. I’m not sure where fraud comes in. If you’re assuming that things are fully developed at 48 months but they continue to develop beyond that you likely want a completion factor, but the same would be true at 60 months, etc.
Let say a scenario that one person use 60 months development period, but the claims after 48 months is rarely occurred. How can one convince the other person that it is better to construct a triangle with 48 months period ?
To answer your question first indirectly, I’ll start with a counter argument to what you’re proposing:
If all I had access to was 48 months of development, I would agree with you. Even with knowledge that some claims might take longer to develop.
However, if I had access to 72 months of development–which will generally indicate the full development at 60 months was achieved–why not use it all?
to answer your question more directly, what you should to is compare how material the additional development for those infrequent claims would be for both the line under review and for the company. If this amount is very small overall–but looking that far out would generate volatile development factors–that might be an argument for using the shorter development assumption and do some analysis for a contingency provision for those rare occasions of a longer-developing claim.
Why do you want to convince the other person that 48 months is better? Surely we just want the best estimates we can get?
I’m guessing you’ve got some tradeoff between recency of data and comprehensiveness of data, which is a common tradeoff. If claims after 48 months are rare maybe you can just throw a completion factor of 1.02 or something and call it a day if doing so results in a more material benefit from responding to the more recent information quicker?
I sense that you are a student, and English might not be your first language.
Here is a very general, textbook type of approach.
Well, a common practice, I will suggest, is that you can use your Chain Link for the length of your triangle. But then you have to make a judgement about what happens after your triangle, and call that a “judgemental tail factor”
So if you have 60 months of triangle data, you can determine the development through 60 months. But you have to estimate an extra factor for 60 to ultimate.