Reported Case Reserves

What a Reported Case Reserve Measures

When a claim has been reported, the insurer can estimate the payments still expected on that particular claim. The estimate recorded for the claim is its case reserve. Because it is based on the information available for an identified claim file, it is a claim-level estimate, not a total for claims that have not yet been individually reported.

A case reserve is measured at a specified valuation date. It can change as the insurer receives new information, makes payments, or revises its assessment of the claim. For an aggregate to be meaningful, each individual amount must use the same valuation date, coverage scope, currency, and basis for expenses. The examples below treat amounts as loss only and exclude loss adjustment expenses (LAE).

Definition: For a reported claim $i$, the case reserve $R_i$ is the estimate, at a stated valuation date, of the unpaid loss payments remaining on that claim. The paid loss $P_i$ is the cumulative loss paid on the claim by that date. The reported incurred loss for the claim is $P_i+R_i$. A case reserve may be recorded directly as an estimate of remaining payments or calculated as a claim-level estimate of ultimate loss less cumulative paid loss.

These terms refer to different amounts. Paid loss describes payments already made; the case reserve describes estimated future payments on reported claims; reported incurred loss combines the two. If an estimate of ultimate loss is used, it must be clear whether that estimate is before or after payments already made. Adding paid loss to an estimate of remaining payments would count paid amounts twice.

Calculating and Aggregating Claim-Level Reserves

If a claim file gives an estimate of ultimate loss, denoted here by $U_i$, and cumulative paid loss $P_i$, then the remaining case reserve is the difference. This calculation is valid when both amounts refer to the same claim, valuation date, coverage, and loss basis, and $U_i$ includes payments already made.

$$ R_i=U_i-P_i $$

The total reported case reserve for a set of claims is the sum of their individual case reserves. The total is not the sum of their ultimate estimates unless no payments have been made.

R_{\text{total}}=\sum_{i=1}^{n}R_i

The calculation can be checked by reconciling the aggregate reported incurred loss: total paid loss plus total case reserve must equal the sum of the claim-level ultimate estimates, when those estimates are defined on the same basis.

\sum_{i=1}^{n}U_i=\sum_{i=1}^{n}P_i+\sum_{i=1}^{n}R_i

Worked Example: Calculating Reserves for Four Reported Claims

A hypothetical insurer values four reported property claims at year-end. For each claim, the file lists cumulative paid loss and the current estimate of ultimate loss. Calculate each case reserve and the total case reserve. All amounts are loss only, in dollars, and use the same valuation date. Assume no discounting (equivalently, an effective annual interest rate of $i=0$ for this calculation); mortality is not modeled. These are deterministic file estimates, not values generated by a probability distribution.

Method. For each file, subtract cumulative paid loss from the estimate of ultimate loss.

\begin{aligned} R_1&=\$31{,}500-\$12{,}000=\$19{,}500,\\ R_2&=\$15{,}250-\$4{,}750=\$10{,}500,\\ R_3&=\$8{,}600-\$0=\$8{,}600,\\ R_4&=\$50{,}000-\$23{,}400=\$26{,}600. \end{aligned}

Now sum the four remaining estimates:

R_{\text{total}}=\$19{,}500+\$10{,}500+\$8{,}600+\$26{,}600=\$65{,}200.

Check. Total paid loss is $\$12{,}000+\$4{,}750+\$0+\$23{,}400=\$40{,}150$. Total estimated ultimate loss is $\$31{,}500+\$15{,}250+\$8{,}600+\$50{,}000=\$105{,}350$. The reconciliation is $\$40{,}150+\$65{,}200=\$105{,}350$, as required. The common mistake avoided is adding paid loss to the ultimate estimates and calling the result a reserve: paid amounts are already included in ultimate loss.

Why the Aggregate Reconciliation Holds

The relationship between total paid loss, case reserves, and estimated ultimate loss follows directly from the claim-level definition. For each claim, the estimate of ultimate loss consists of the amount already paid plus the amount still reserved. Adding that identity over all claims gives the aggregate identity. It is a bookkeeping reconciliation, not a guarantee that the estimates will equal the payments ultimately made.

Start with one claim.
On the stated basis, claim $i$'s estimated ultimate loss is its cumulative paid loss plus its remaining case reserve: $U_i=P_i+R_i$.

Rearrange for the reserve.
Subtract paid loss from both sides to obtain $R_i=U_i-P_i$.

Sum over the claims.
Adding the claim-level identities gives $\sum_i U_i=\sum_i P_i+\sum_i R_i$. Thus, aggregate case reserves equal the sum of the claim-level remaining estimates.

This reasoning depends on consistent definitions. For example, if one file's estimate includes a category of expense while the others exclude it, the aggregate may still be arithmetically calculable but will not represent a uniform loss-only total. Similarly, amounts from different valuation dates should not be added without first bringing them to a common date and basis.

Worked Example: Reconciling Reserves Between Two Valuation Dates

A hypothetical insurer tracks three reported liability claims. The table gives cumulative paid loss and estimated ultimate loss at two valuation dates. Calculate total case reserves at both dates and the signed change, defined as current total minus prior total. Amounts are loss only and in dollars. Assume no discounting ($i=0$ for this calculation); mortality is not modeled. The file estimates are deterministic, with no probability distribution assumed.

Claim	Prior paid	Prior ultimate	Current paid	Current ultimate
A	$8,000	$30,000	$14,000	$34,000
B	$5,000	$20,000	$9,000	$24,000
C	$2,000	$13,000	$4,000	$10,000

Prior valuation date. Subtract prior cumulative paid loss from prior estimated ultimate loss for each claim:

\begin{aligned} R_{A,\text{prior}}&=\$30{,}000-\$8{,}000=\$22{,}000,\\ R_{B,\text{prior}}&=\$20{,}000-\$5{,}000=\$15{,}000,\\ R_{C,\text{prior}}&=\$13{,}000-\$2{,}000=\$11{,}000,\\ R_{\text{prior}}&=\$22{,}000+\$15{,}000+\$11{,}000=\$48{,}000. \end{aligned}

Current valuation date. Use current cumulative paid amounts, not just payments made since the prior date:

\begin{aligned} R_{A,\text{current}}&=\$34{,}000-\$14{,}000=\$20{,}000,\\ R_{B,\text{current}}&=\$24{,}000-\$9{,}000=\$15{,}000,\\ R_{C,\text{current}}&=\$10{,}000-\$4{,}000=\$6{,}000,\\ R_{\text{current}}&=\$20{,}000+\$15{,}000+\$6{,}000=\$41{,}000. \end{aligned}

The signed change is current minus prior:

\Delta R=\$41{,}000-\$48{,}000=-\$7{,}000.

Thus, total case reserves changed by $-\$7{,}000$, a decrease of $\$7{,}000$. The check is also available from the aggregate identity: estimated ultimate loss rose from $\$63{,}000$ to $\$68{,}000$, an increase of $\$5{,}000$, while cumulative paid loss rose from $\$15{,}000$ to $\$27{,}000$, an increase of $\$12{,}000$. Therefore the reserve change is $\$5{,}000-\$12{,}000=-\$7{,}000$. This example avoids the sign trap of describing a negative change as a negative-sized “decrease”; the signed change is negative, while the amount of the decrease is positive.

Case Estimates as Expected Future Payments

A claim-level estimate need not always be a single certain amount. An adjuster or analyst may consider multiple possible future payment outcomes and assign probabilities to them. If the reserve basis calls for an expected payment, the case estimate is the probability-weighted average of those outcomes. This is one way to express uncertainty; it does not mean that the final payment must equal the calculated average.

Worked Example: Probability-Weighted Estimates for Two Claims

At a valuation date, an analyst considers future loss payments on two hypothetical reported claims. For claim A, the possible remaining payments are $0 with probability 0.20, $20,000 with probability 0.50, and $60,000 with probability 0.30. For claim B, they are $10,000 with probability 0.40 and $30,000 with probability 0.60. Calculate each expected remaining payment and their total. Assume the listed probabilities are the full discrete distributions for each claim, payments are not discounted ($i=0$), and mortality is not modeled.

Claim A. Multiply each payment by its probability and add the products:

R_A=(0.20)(\$0)+(0.50)(\$20{,}000)+(0.30)(\$60{,}000) =\$0+\$10{,}000+\$18{,}000=\$28{,}000.

Claim B. Its expected remaining payment is:

R_B=(0.40)(\$10{,}000)+(0.60)(\$30{,}000) =\$4{,}000+\$18{,}000=\$22{,}000.

Therefore, the total case estimate on this expected-payment basis is $\$28{,}000+\$22{,}000=\$50{,}000$. The probabilities for claim A sum to $0.20+0.50+0.30=1.00$, and those for claim B sum to $0.40+0.60=1.00$, so each is a valid distribution. Linearity of expectation means the expected aggregate is the sum of the individual expectations; independence between the claims is not required. The common mistake avoided is averaging the possible payment amounts without weighting them by their probabilities.

Interpretation and Common Exam Traps

Case reserves are useful because they connect claim-file estimates to reported incurred amounts and make it possible to aggregate the estimated unpaid payments on reported claims. However, the aggregate is only as consistent as the individual file amounts and the rules used to construct them. A reserve total is not, by itself, proof that the estimate is adequate or that future payments will match it.

Confusing reserve with ultimate loss. If ultimate loss includes cumulative payments, subtract paid loss to find the remaining case reserve.
Using incremental instead of cumulative paid amounts. When calculating a reserve at a valuation date, use all payments made through that date.
Mixing dates or scopes. Aggregate estimates only when they refer to the same valuation date and include the same types of loss and expense.
Misstating a signed change. Calculate current minus prior. A result of $-\$1{,}000$ is a change of negative $1,000, or a decrease of $1,000.
Assuming the reconciliation proves accuracy. The equality of paid loss plus case reserve and estimated ultimate loss follows from the definitions; it does not establish that the estimate will prove correct.

Key takeaway: For each reported claim, case reserve is the estimated unpaid loss at the valuation date. Calculate it directly from the remaining-payment estimate or as estimated ultimate loss less cumulative paid loss, then sum the claim-level amounts on a consistent basis.

Check Your Understanding

For each problem, calculate the requested amount using the stated valuation date and basis.

A reported equipment claim has estimated ultimate loss of $48,000 and cumulative paid loss of $17,500. What is its case reserve? (Answer: $30,500)
Two reported claims have direct remaining-loss estimates of $12,750 and $6,250. What is the total case reserve? Assume both estimates are at the same valuation date and exclude LAE. (Answer: $19,000)
A portfolio's total case reserve was $36,000 at the prior valuation date. At the current date, its individual claim reserves sum to $39,500. What is the signed change, and did reserves increase or decrease? (Answer: +$3,500, an increase of $3,500)
For a claim, estimated ultimate loss increases by $4,000 between valuation dates while cumulative paid loss increases by $9,000. If the prior case reserve was $54,000, what is the current case reserve and how much did it change? (Answer: $49,000; change of −$5,000, a decrease of $5,000)
A claim's future payment is $5,000 with probability 0.25, $25,000 with probability 0.50, and $45,000 with probability 0.25. On an undiscounted expected-payment basis, what case estimate does this distribution give? (Answer: $25,000)

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