Ultimate paid > ultimate incurred is bad

I’m afraid i don’t recall exactly, but i’ve seen some internal to my organization literature or comments in the files themselves, that during the reserving exercise, a paid development ultimate loss method is given no weight/discarded entirely because the ultimate loss amount from paid development was greater than the ultimate loss from an incurred development method.

I feel like I’ve reviewed this before, but why is that inherently bad?

Till all are one,


No answer to your question but crosspost to annoyed thoughts… Your username is spelled differently than your typed out name… Was there someone who already registered Epistemus? Can you ask a mod to change your username to the correct spelling?

Can’t tell you why it’s inherently bad, don’t think anyone can. I can guess why it’s probably bad by making some assumptions.

Incurred inherently has more information than paid, since incurred is paid + case.
It’s also relatively stable if people setting your case reserves are smart.

If paid ultimate > incurred ultimate, it’s likely due to volatility with no underlying meaning.

Yeah, the truth is i misspelled it when registering, Epistemus is who i’d prefer my pretend name be on this platform. I’m going to make a separate post in a site feedback forum.

My bad.

Hey, i can change your user name. Let me know if that’s not what you want.

I can think of reasons why paid development would be more than incurred, and be the best estimate, though. If case reserves are weakening, and you use the chain ladder technique, you can dramatically underestimate the ultimate. Paid dollars may still give a reasonable estimate. That’s especially true of a line like workers compensation, where the payments are largely driven by exterior forces (like laws and hospitals) and the claims department doesn’t have a great deal of influence over their timing.

Glenn Meyers told me one of the first things he did at ISO was switch from incurred to paid for industry projections. ISO used to estimate severity trend from incurred data, way back when. And their estimates varied widely from year to year. (This was back in the late 1900’s when inflation was a big deal.) He moved to paid industry data, and suddenly they produced trends that held up. It turns out that case reserve adequacy is highly correlated across the industry.

In general, paid data is more “real”, but subject to random noise. Incurred data carries more information, and is less noisy, but also more subject to bias. If i have a smaller data set, i always pay attention to incurred. If i have a large enough data set, i give a lot more weight to paid.


Incurred data includes “someone’s” best estimate for what’s left to be paid.

For short tailed lines, I’d expect ultimates to be close between paid and incurred data.

For longer tailed lines, I consider how mature the paid data is as well as looking at changes in claim behavior or benefit levels when deciding how much give weight to give to either paid or incurred data. For example, very rarely will I consider paid data for the two most recent AY (although I still calculate it).

For “primary insurer” lines of business (e.g., private passenger auto and homeowners), the incurred and paid estimates can help give a good range for the “final” answer.

Ah yes, this can indeed happen, and can swing in all 4 directions (case reserve adequacy can strengthen or weaken, as can payout speed)

Lucy, etc. give good answers on the real life concerns, but I believe Exam 7 goes over the concept that having negative development is undesirable for GLMs, but that’s really a GLM limitation rather than a real world issue.

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Really strong answers here, but the most important takeaway is this JSM statement.

Try not to fall into any hard and fast rules. This “reasoning” could ultimately create a downward bias on your estimates since a potentially valid estimate is ignored when it’s higher than another. Dig into the reasons why it might be higher (like all that Lucy described) and whether those reasons are reasonably reflective of reality and future expectations.

Yes, age matters. I would tend to look at “expected emergence of the ultimate”, rather than number of years, but I tend to like paid indications for “middle aged” claims.

Very young claims typically have little or no paid information, and the best guess of the claims adjuster is far better than trying to extrapolate from “1% has been paid”. Very mature claims are often fully understood by the claims adjuster, and so long as they are handling mortality in a reasonable way, (or, at least, consistently) incurred data is generally reliable. But in-between, the lower degree of bias from “what’s the claims department’s philosophy this year?” tends to make the paid data more reliable.

Of course, you need to understand what’s driving the variability between estimates the book you are evaluating.

Also, I don’t trust anything chain ladder when the cumulative development factor is greater than 2. There’s just too much leverage from random noise. Paid BF might be useful, or some sort of frequency/severity approach – especially if the existence of claims develops fairly quickly. I don’t know that “2” is the best number for that cut-off, but it’s the one I tend to use, for both paid and incurred development. It comes into play more often for paid, though.