IBNR Allocations

[Doug Wolfe]

At my company we develop IBNR reserves at the company and product level. Then when IBNR reserves are reported at a finer level - such as group v. individual, policy form, state - we'll use inforce premium or, inforce face amount for life products, as the basis of the allocation.
Is anyone aware of more sophisticated methods to allocate IBNR? Any allocation technique which spreads IBNR according to inforce values will surely over-allocate IBNR to the cells where the claims were paid earlier than normal, and under allocate to the cells where the claims get paid later than normal. Perhaps some method is in use or has been described in actuarial literature which would, for example, somehow allocate IBNR in inverse proportion to the volume of claims paid to date. I'd appreciate hearing about any such alternatives.
The best method may end up being simply the premium or face amount allocation, and actuaries simply have to review allocated IBNR values and adjust any "wierd" ones.
I look forward to any feedback. Thanks.

[Dr T Non-Fan]

You're screwed regardless of method.

Choices:
1. Use average completion factors by incurred month against the finer level's claims by incurred month. I wouldn't use one factor, but the set of factors instead.

2. You can estimate IBNR at a finer level by running the finer level's triangle through your IBNR estimator. To equate to a total, you can run each finer level through the estimator, and add or subtract from it some spread to make the sum of IBNR the same as the total IBNR.

If the finer level is too small, then there is nothing you can do.

With less-small levels, some smoothing of larger claims (excluding large claims, and adding a pooling charge) will be necessary.

[Toll Free]

A lot depends on how you're using the allocated reserves. If you're using them for pricing decisions, premium is actually pretty desirable - assuming that you take the expected loss ratio into account when allocating. This effectively pools small, more variable, lines by regressing all cells to the mean. Be sure to allocate on a month-by-month basis, to account for shifts in mix. Some other thoughts:

- Try to account for slow vs. fast-pay claim situations. For instance, inpatient hospital claims should be allocated separately from pharmacy claims, if at all possible. A good example of this would be one state/city/hospital where claims are submitted electronically by the provider, rather than on paper.

- Older claims are more likely to be completions of claims already submitted, rather than "brand new" claims. It therefore makes sense to allocate proportionally based on paid claims after a certain point in time. I'm sure there's some sort of Bornhueter-Ferguson-like method that could be applied.

- I said "Bornhueter".

- I use the method DTNF suggests (run all cells through your IBNR estimator, then balance back to the total reserve estimate) often, especially in estimating trend by component.

- If your deductibles/plan designs vary wildly, you may want to account for seasonality. Then again, this could be over-thinking the issue. If, for example, you're looking at data in 12 month chunks, it's possible (likely?)that the reserve accounts for less than 20% of the incurred claims in your most recent time period. A 10% "error" in your allocation would therefore only impact results by 2%. If you're not happy with that level of error, good luck with health insurance.

A way to diffuse the issue is to try and incorporate some sensitivity/significance testing in your actual/expected analysis (I am assuming that this, in the end, is why you're worried about this). The extra smoothing caused by the allocation will make you feel that much better about the results.

Good luck.

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[Doug Wolfe]

A belated thank-you to Dr. T and Toll-Free! Your comments were very helpful.
-DougWolfe