Claims triangles

I’m not a health actuary, but I play one at work.

I inherited a spreadsheet that has numerous claims triangles for a number of LOBs.

Is there a correct number of months of history/development to use? Right now, we have 48 months of history and then it falls off the table. The spreadsheet was designed to hold 60 months’ worth, but there’s an input item where it’s specified to only use 48.

In order to save on space/computation, I’m probably going to pare down the ranges so that they only use 48 months.

I imagine the answer to my question above is “it depends”…on the credibility and timeliness and tail of your data, but I’d love to hear a discussion about it. Perhaps there are easy-to-obtain & easy-to-read resources you can point me to.

How many claims are you getting at 48 months?

Can you run it once using 60 months to assess the materiality of what you’re missing? Is it close enough to $0 that $0 is a reasonable estimate?

I used claim triangles in disability insurance, which is obviously a much longer-tailed product.

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How long is a piece of string? Haha. I don’t work in health, but in P&C you can have a prior sense from what line of business it is. 48-60 would be fine for property damage, probably taking a chance you’re missing information for casualty though.

If you don’t have any prior view then basically you make a guess using as much data as you can. You can also fit a curve to the development factors you do have to estimate the tail regardless of when it truly ends (this is a topic on CAS Exam 7 in the Clark paper).

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Not health here either. What’s the average closed severity of old claims? Assuming you have those. You can use that to estimate what the ultimate amount should be, assuming no IBNYR.


I’m assuming your triangles aren’t old enough to to see any ultimate amounts, which means you’ll need to fit a curve on the available LDFs to extrapolate on the tail factor.

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I’m p&c, and I’ve mostly worked on long tail lines, and i don’t think I’ve ever used a triangle with as few as four years outside of a fake example for teaching purposes.

That being said, a triangle should extend our far enough that the development it doesn’t pick up is insignificant, or until you run out of data, or until there was some massive change that renders the old data unhelpful in the triangle, whichever is the limiting factor.


Health actuary here, not in valuation but I do some independent completion analysis for my work.
Just look at your 3, 4, 5 year lag experience. Decide if that experience makes a difference in your calculations, or even if there is a predictable pattern.
Most of the experience will be adjustments, when someone in claims decides to audit eligibility or overpayments to hospitals.


I’ll just toss out: there’s something reassuring in having a big enough triangle that you have 1.0 development factors in your last column.


Is that 1.0 a rounded-down 1.049 or a rounded-up 0.951?


Basically a tax refund at that point