Convert AY payment pattern to UW Year Pattern

Professional Actuarial Topics Property/Casualty
1

Hi All,

For some reason this is tripping me up and I’m almost embarrassed to ask. How would one go about converting an AY liquidation pattern to an Underwriting year pattern? I’m trying to convert some analysis that was assuming a loss occurring basis to one assuming risks attaching.

Thanks for any help or reference material.

Regards,
accidental_actuary

2

How granular is the payment pattern? Do you have it every quarter? Every year?

Do you have a pattern of how risks attach during the CY?

3

The AY pattern itself is annual and we can assume the risks attach uniformly through the CY year.

So let’s say we had $4000 of incurred losses in the AY that came from $1000 each quarter and the annual pattern tells us how much of the $4000 was paid in the first year.

Instead of the losses occurring, we’re assuming risk attaching. Then I think we are looking at $250 of incurred losses in Q1, $500 in Q2, $750 in Q3, and $1000 in Q4 as we earn into the risks. It feels like there should be a general adjustment that we can make to the AY pattern to account for the shift in perspective.

4

You adjust for the difference in age at average accident date. Average accident date for AY is 6 months, and it’s 12 months for PY. Add or subtract 6 months (depending on which way you’re going). 12 month AY = 18 month PY because both are 6 months after the average accident date.

5

Thank you for the help. To make sure I understand, we would expect to see the same amount of relative loss at 12 months for the PY as we see at 6 months for the AY? If I wanted to know the relative amount of loss paid in a given calendar year, then the AY’s line up as the average accident date is 6 months. This is what I have to start with, an AY pattern assuming mid-year payments. Under the PY assumption, should I simply interpolate the AY pattern? The amount paid in the first year would effectively be the 3 month amount under the AY and 15 months for the second year and so forth? In other words, the amount paid in the first year under PY assumption would be half that paid under the AY assumption and the amount paid in the second year would be the average of the 1st and 2nd years?

6

If you only have an AY pattern, and you need a PY LDF for age X, you use the AY LDF for age x - 6. That’s it.

That’s the assumption. However, I wouldn’t rely on this adjustment too much for early and partial maturities. If you really need a 12 month to ultimate PY LDF, you should do more to validate that the adjustment is reasonable.