ULAE¶

This is taken on CY basis

Dollar-based Techniques¶

ULAE costs track with claim costs in both timing (both have similar payment patterns) and amount (a single $10,000 claim has the same ULAE as ten $1,000 claims)

Classical¶

CY basis, Paid amounts
For each CY, ULAE Ratio, $W = \dfrac{\text{ULAE}}{\text{Loss \& ALAE}}$
Trends? and Outliers?
Select $W^*$

$W^*$ is not a good estimate of $W_{\text{true}}$

Book is growing/shrinking (it should be in steady state)
Particularly Long tailed LOB

\[ \text{Unpaid ULAE} = W^* \times [\text{Pure IBNR}+ 50\% \times (\text{Case} + \text{IBNER})] \]

Estimate of future paid claims on unreported losses = Pure IBNR
For Open Claims, some ULAE is already paid (assume 50% of it to open it)
- Case reserves
- Development on known claims (IBNER)

All IBNR is pure IBNR $\implies$ IBNER=0

Mango-Allen¶

For each CY, ULAE Ratio, $W = \dfrac{\text{ULAE}}{E(\text{Loss \& ALAE})}$

Kittel¶

For each CY, ULAE Ratio, $W = \dfrac{\text{ULAE}}{Avg(\text{Paid},\text{Reported})}$

Generalized¶

(R) Opening $\to$ Ult cost of "Opened" (Reported) during CY
(P) Maintaining $\to$ Paid during CY
(C) Closing $\to$ Ult Cost of "Closed" during CY

\[ B = U_{1}R + U_{2}P + U_{3}C \]

$M$ = Paid ULAE
$W = \dfrac{M}{B}$ $\to$ Select $W^*$

$L$, the ultimate losses of the same group of accident years will be given. And we have to find the unpaid losses.

BF: $(L - M) \times W^*$
Dev and Expected Claims are flawed.

Connection¶

Classical & Kittle: $U_{1} = 50\%$, $U_{2} = 0\%$ and $U_{3}=50\%$
- No cost of maintenance
Assume no partial payments, Paid $\impliedby$ Closed
- So, $C = P$ (Closing the claim = paid during CY)