Claim Reserve

Study guides: Exam CP-321, Exam GH-201C, Exam GH-201U

A claim reserve is the liability a health or group insurer holds at the valuation date for benefits on claims incurred on or before that date but not yet paid — reported claims still in course of settlement, claims incurred but not reported (IBNR), and, on disability and long-term care claims, the present value of benefits not yet due. It is the health counterpart of P&C unpaid claims, and it is distinct from the non-claim reserves (policy, unearned premium and premium deficiency reserves) held for coverage not yet provided.

$\hat{C}_m = \frac{P_m}{CF_{k(m)}}$

$\hat{R} = \sum_m \left(\hat{C}_m - P_m\right)$

$\text{DLR} = \sum_{t \geq 0} v^{t}\, {}_{t}p^{\,d}\, B_t$

Completion factor method (short-duration medical, dental, drug): $P_m$ is claims incurred in month $m$ and paid to date, $k(m)$ the months of lag since $m$ , and $CF_k$ the share of ultimate incurred claims paid by lag $k$ , read off a lag triangle as the reciprocal of the product of the remaining age-to-age factors. It is the chain ladder stated as a percentage complete.
For the most recent incurral months $CF_k$ is small, so $1/CF_k$ magnifies any noise in $P_m$ . Practice replaces those months with a projection (expected PMPM $\times$ members, trended), or blends the two.
Disabled life reserve (LTD, LTC, waiver of premium): for an open claim, $B_t$ is the benefit due at time $t$ and ${}_tp^{\,d}$ the probability the claimant is still disabled (claim termination by recovery or death). CP-321 names the pieces for long-duration contracts: the present value of amounts not yet due (PVANYD), claims in course of settlement (ICOS) and IBNR.
ASOP 5 defines the unpaid claims liability as the unpaid portion of incurred claims, including unreported and reported-but-unpaid claims. Environmental changes — trend, seasonality, claim processing speed — distort completion factors, which is why the syllabus asks you to evaluate them.

Completion Factor Reserve with a Projected Recent Month A medical plan values claims at May 31. Cumulative paid claims ( $\$000$ ) by incurral month and lag in months:

Incurred Lag 0 Lag 1 Lag 2 Lag 3 Lag 4

Jan 420 860 960 990 1,000

Feb 400 830 925 955

Mar 450 920 1,030

Apr 430 880

May 470

Claims are complete by lag 4. Using volume-weighted age-to-age factors, compute the claim reserve. Then replace May with a projection of $\$101.50$ PMPM on $10{,}200$ members.
Answer Age-to-age factors, then completion factors (product of the remaining factors, inverted):
 $\begin{align*} f_{0 \to 1} &= \tfrac{3{,}490}{1{,}700} \\ &= 2.0529 \\ f_{1 \to 2} &= \tfrac{2{,}915}{2{,}610} \\ &= 1.1169 \\ f_{2 \to 3} &= \tfrac{1{,}945}{1{,}885} \\ &= 1.0318 \\ f_{3 \to 4} &= \tfrac{1{,}000}{990} \\ &= 1.0101 \end{align*}$ 
$CF_4 = 1$ , $CF_3 = 0.9900$ , $CF_2 = 0.9595$ , $CF_1 = 0.8591$ , $CF_0 = 0.4185$ . Reserve by month, $P_m(1/CF - 1)$ :
 $\begin{align*} \text{Feb} &= 955/0.9900 - 955 \\ &= 9.6 \\ \text{Mar} &= 1{,}030/0.9595 - 1{,}030 \\ &= 43.5 \\ \text{Apr} &= 880/0.8591 - 880 \\ &= 144.3 \\ \text{May} &= 470/0.4185 - 470 \\ &= 653.1 \\ \hat{R} &= 850.5 \end{align*}$ 
May's completion estimate implies $1{,}123.1/10.2 = \$110.10$ PMPM, well above the projection. Replacing May:
 $\begin{align*} \hat{C}_{\text{May}} &= 10{,}200 \times 101.50 / 1{,}000 \\ &= 1{,}035.3 \\ \hat{R} &= 197.5 + (1{,}035.3 - 470) \\ &= 762.8 \end{align*}$ 
The reserve is $\$762.8$ K rather than $\$850.5$ K. With only 42% of May paid, an unusually fast first month of payments was being multiplied by $2.39$ ; the projection gives that month the weight its data deserves.

Incurred	Lag 0	Lag 1	Lag 2	Lag 3	Lag 4
Jan	420	860	960	990	1,000
Feb	400	830	925	955
Mar	450	920	1,030
Apr	430	880
May	470

Disabled Life Reserve on an Open LTD Claim A disabled claimant receives $\$36{,}000$ a year, paid at the start of each year, for at most three more payments. The probabilities the claim is still open at times $1$ and $2$ are $0.80$ and $0.68$ . At $4\%$ interest, compute the reserve for amounts not yet due.
Answer
 $\begin{align*} \text{DLR} &= 36{,}000\left(1 + 0.80v + 0.68v^{2}\right) \\ &= 36{,}000\,(1 + 0.7692 + 0.6287) \\ &= 36{,}000 \times 2.3979 \\ &= 86{,}325 \end{align*}$ 
The reserve is $\$86{,}325$ . Ignoring claim terminations would give $\$103{,}899$ — termination rates, not interest, drive this reserve.

How it appears on the exam

GH-201U and GH-201C (objective 3, "calculate appropriate claim reserves given data"): a lag triangle of paid claims plus membership, asking for completion factors, the reserve, and a judgement on the most recent months — usually blended with a PMPM projection.

GH-201 objective 4 pairs the calculation with an environmental change (a processing backlog, a seasonal spike, a trend shift) and asks how the factors and reserve move, in writing.

"Describe the types of claim reserves" (GH-201 objective 1) is a written list: reported but unpaid, IBNR, PVANYD on long-duration claims, and claim adjustment expense, set apart from non-claim reserves.

CP-321 objective 4 moves to long-duration contracts: a disabled life or LTC claim reserve from termination rates and interest, alongside policy and premium deficiency reserves.

Exam traps

Inverting the wrong way: a completion factor is below $1$ and you divide paid by it. Multiplying gives a reserve that is negative.

Trusting lag-0 completion: dividing a recent month by a factor near $0.4$ turns a 10% blip in paid into a 10% error in that month's ultimate. Projection or blending is expected for recent months.

Not adjusting for a processing speed-up: faster payment raises recent paid amounts, and historical completion factors then overstate the reserve.

Calling a disabled life reserve IBNR: the claim is reported; its future benefits are amounts not yet due, valued with termination rates.