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Run-off Triangles: Underwriting year and Accident year based Triangles

N

Naga Sai Shivanee

Member
Hi
I have a doubt regarding the underwriting year and accident year based Triangles.

Consider that two triangles are built for the same data. One is based on underwriting year and the other is accident year. Accident year development triangle tends to have a faster run off/greater development factors than the underwriting year development triangle. Why is it so?

Thankyou in advance.
 
Consider the lifetime of a claim on a policy:
1) the policy is underwriting
2) an accident happens
3) a claim is reported to the insurer in respect of an accident
4) the insurer pays out the claim

The delay between 2 and 3 (or 4) corresponds with how far along the row of an accident year incurred (or paid) claims triangle a claim appears. The row in question will be the row for the accident year in which the date of 2 falls.
The delay between 1 and 3 (or 4) corresponds with how far along the row of an underwriting year incurred (or paid) claims triangle a claim appears. The row in question will be the row for the underwriting year in which the date of 1 falls.

For example:
A policy is written in June 2014, then an accident happens in Jan 2015 which leads to a claim being reporting to the insurer in Feb 2015 and it's paid out in Feb 2016.

This claim will appear in the 2014 row of an underwriting year paid claims triangle, in the third development year (third column, say) corresponding to payment in 2016. It will appear in the 2015 row of an accident year paid claims triangle, in the second develop year (second column) corresponding to payment in 2016.

I've oversimplified here, but hopefully this explains why the rows of an accident year triangle tend to 'develop' quicker. The distance of every single claim in the triangle from the start of the row is shorter for an AY triangle, because the row only 'starts' at time 2 (as defined above), whereas for an underwriting year triangle the row starts at time 1.
 
So is it fair to say that for an AY incremental payments triangle, DY 0 for a certain year will capture accidents ranging from Jan 1st of the year up to Dec 31st of that year and hence payments from Jan 1st of the AY up till Dec 31st of the next calendar year?

Whereas for an UY incremental payment triangle, DY 0 for a certain year will capture accidents ranging from Jan 1st of the year up to Dec 31st of the next calendar year and hence payments from Jan 1st of the UY up till Dec 31st of the calendar year two years later? I guess that would mean that for DY 0 of an UW year in an incr claims paym triangle, payments across calendar years would then be roughly split 25/50/25 into cal year = UW year/next calendar year/year after?

Many thanks in advance.
 
Hi
I don't think that's how it works.
In Accident Year X Development Year 0, the figure in the run-off triangle shows the claims paid in calendar year X in respect of accidents that occurred in calendar year X.
In Underwriting Year Y Development Year 0, the figure in the run-off triangle shows the claims paid in calendar year Y in respect of policies that started in calendar year Y.
Hope that helps.
 
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