Evaluation¶
Retroactive testing¶
Why check unpaid estimates?
- If there has been a change in exposures, then the unpaid estimates have to be updated.
- "Are claims developing as expected, or are there any surprises?"
- A diagnostic to check if unpaid claim estimates are reasonable.
- Actual vs expected = Retroactive testing
What if actual development \(\gt\) expected development? (HUGH WHITE). Options are:
1. Reduce IBNR (speedup in reporting) Expected Claims
2. Leave IBNR unchanged (large reported claim, black swan). Future is as per expectation. B-F
3. Increase IBNR. (deterioration of claims ratio). Development
Expected Emergence¶
Expected Reported Claims between \(t\) and \(t+1\)
- This formula preserves current IBNR/unpaid claims
- %rept or %paid = 1/CDF
Development for Ultimate estimates¶
Then the following are equivalent to Expected Reported Claims between \(t\) and \(t+1\)
- \(\text{Cum. rept claims}_{t} \times \left(LDF_{(t,t+1)} -1\right)\)
- \(\text{Ult Claims} \times(\%Rept_{t+1} - \%\mathrm{Re}pt_{t})\)
Interpolation¶
- Linear interpolation within a quarter \(\to\) more reasonable expected emergence estimate than that within an entire year.
- \(\impliedby\) Development higher for earlier maturities and decreases over time.
- Linear interpolation assumption is not reasonable for prolonged periods
- Most development will tend to occur earlier in the year than later in the year.