Why the Loss Basis Must Be Explicit
A loss amount is not fully described by a dollar figure alone. It also depends on what has been paid, what is reserved, what future payments are estimated, and the valuation date. For example, a claim with $10,000 paid and $6,000 in outstanding case reserves has a different case-incurred amount from its ultimate estimate if the claim is expected to require further payments.
The three bases used here are cumulative paid losses, case-incurred losses, and ultimate losses. Each answers a different question. Paid losses describe payments made by a specified date; case-incurred losses add the current case reserves for reported claims; ultimate losses estimate the total covered loss expected to emerge for the defined population. They cannot be compared or reproduced reliably unless their scope and valuation conventions are stated.
These definitions assume the same coverage, claim population, currency, and gross-or-net treatment are being used throughout. State whether amounts include allocated loss adjustment expenses, deductibles, salvage, subrogation, or other recoveries. Such items can be handled differently across data systems; the key is to define the treatment consistently. All examples below are hypothetical accounting illustrations. No interest rate, mortality assumption, or probability distribution is required: the calculations use the stated dollar records and estimates.
Paid and Case-Incurred Losses
Paid loss is a cash-based measure. It includes cumulative payments through the valuation date, not merely the payments made during a single month or quarter. If a claim has no payment by that date, its paid amount is zero even if a reserve has been established.
A case reserve is the insurer's estimate, at a particular date, of the remaining amount expected to be paid on a reported claim. It is a snapshot, not a payment. A reserve can increase or decrease as information changes, and it can be released when a claim closes. The reported-claim case-incurred amount adds this snapshot to cumulative paid loss.
The identity is an accounting construction. The cumulative paid portion records what has already been paid; the outstanding case reserve estimates the remaining amount currently recognized for that reported claim. Adding the two produces the paid-to-date amount plus the currently reserved unpaid amount. It does not establish that the claim's final cost will equal the incurred amount.
Worked Example: Building Case-Incurred Loss From Claim Records
A hypothetical insurer values four reported claims at June 30. The records contain cumulative covered payments of $12,400, $8,750, $0, and $4,300. The respective outstanding case reserves are $3,600, $6,250, $9,100, and $0. Calculate total paid and case-incurred losses. Assume all amounts are on the same gross basis and exclude expenses and recoveries.
Method. Sum the cumulative payments first:
Total paid loss is $25,450. The third claim has no payment yet, but its reported status and $9,100 case reserve mean it contributes to incurred loss.
Next sum the outstanding case reserves:
Add the two components:
Total case-incurred loss at June 30 is $44,400. As a check, the claim-level incurred amounts are $16,000, $15,000, $9,100, and $4,300; their sum is also $44,400. A common mistake is to omit the unpaid reported claim because its paid amount is zero. That would understate incurred loss by $9,100.
Ultimate Losses: A Different Estimate
Ultimate loss is an estimate, not simply another name for paid or case-incurred loss. For a reported claim, an ultimate estimate includes paid amounts to date and the estimated remaining covered loss. The estimate of remaining loss may differ from the case reserve: the case reserve is the current claim-level estimate recorded in the system, while the ultimate estimate may reflect additional expected development on reported claims. For a portfolio, ultimate loss may also include estimated losses from claims that have occurred but are not yet reported.
A useful reconciliation separates the components of unpaid ultimate loss. Depending on the reserving terminology used, estimates for reported claims may include amounts beyond their current case reserves, often described as additional development on reported claims. Claims not yet reported may contribute an unreported-claim estimate. Those categories must be defined consistently to avoid omitting an amount or counting it twice.
The formula is a way to organize the estimated total, not a prescribed estimation method. A reported-claim incurred total is paid to date plus case reserves; it should not automatically be treated as ultimate. Nor should an unreported-claim estimate be added if the supplied ultimate figure already includes it.
Worked Example: Reconciling Case-Incurred and Ultimate Amounts
A hypothetical small commercial portfolio is valued at September 30. For reported claim A, cumulative paid loss is $30,000 and the case reserve is $10,000; the claim-level ultimate estimate is $52,000. For reported claim B, paid loss is $18,000, the case reserve is $7,000, and the claim-level ultimate estimate is $31,000. The portfolio estimate for claims incurred but not yet reported is $17,000. Calculate paid loss, reported-claim case-incurred loss, and portfolio ultimate loss. All amounts exclude expenses and recoveries and use the same gross basis.
Method. First add the paid amounts:
The reported-claim case reserves total:
Therefore reported-claim case-incurred loss is:
Next, sum the two claim-level ultimate estimates:
The reported claims' expected unpaid amounts are $52,000 - $30,000 = $22,000 for claim A and $31,000 - $18,000 = $13,000 for claim B, for total expected unpaid loss of $35,000. This exceeds the $17,000 in case reserves by $18,000, reflecting expected additional loss on the reported claims in this hypothetical estimate.
Finally add the $17,000 estimate for claims not yet reported:
Portfolio ultimate loss is $100,000. The reconciliation also checks as $48,000 paid + $35,000 expected unpaid on reported claims + $17,000 for not-yet-reported claims = $100,000. A common mistake is to add $17,000 of case reserves to the $83,000 of reported-claim ultimate loss, then add the unreported estimate. The $83,000 already includes paid amounts and all estimated remaining loss on the reported claims, including the case reserves; adding those reserves again double counts them.
Reproducibility: What Must Be Present?
To reproduce a loss basis, a reviewer needs enough information to reconstruct both the amount and the definition used. A total alone is insufficient: the same total could have been produced from different claim populations, dates, or gross/net conventions. The required components differ by basis.
| Basis | Minimum components to reproduce it | Important definition choices |
|---|---|---|
| Paid | Claim identifiers; payment transactions and amounts; transaction dates; valuation date; rules for reversals and recoveries | Coverage and claim scope; gross or net; treatment of expenses; currency |
| Case-incurred | All paid-basis components; claim-level outstanding case reserve values as of the valuation date | Reported-claim population; reserve snapshot date; consistent scope and expense/recovery treatment |
| Ultimate | Paid amounts; estimates of remaining loss; defined reported and unreported claim components; valuation date and estimation basis | Whether unreported claims are included; treatment of additional reported-claim development, expenses, and recoveries |
For paid amounts, transaction detail matters. A system extract should distinguish payments from reserve changes and should show how voided, reversed, or recovered amounts are treated. The valuation date must be applied to transaction dates using a stated convention. Otherwise, two analysts might include different transactions while both claim to report “paid through September 30.”
For case-incurred amounts, the case reserve must be a snapshot at the same valuation date as the paid amount. A later reserve snapshot combined with earlier paid data does not reproduce a coherent as-of-date incurred total. Claim identifiers are also important: they allow paid transactions and reserve records to be matched to the same reported claims and help prevent duplicate counting.
For ultimate amounts, the estimate and its scope must be reproducible as well. At minimum, retain the valuation date, the population included, the reported and unreported components, and the estimation basis or assumptions that produced the estimates. This tutorial defines those components; it does not prescribe a loss development procedure. An ultimate estimate cannot be reconstructed from paid and case-incurred totals alone without further assumptions or estimation information.
Valuation-Date Changes and Common Traps
Paid and case-incurred amounts are both date-dependent. As time passes, cumulative paid loss generally changes when payments are made. Case reserves can move in either direction. Consequently, the change in incurred loss between two valuation dates is not generally equal to the change in paid loss, nor is it equal to the reserve change alone.
Worked Example: Comparing Two Reserve Snapshots
A hypothetical insurer reviews three reported claims at January 31 and April 30. The January 31 cumulative paid amounts for claims P, Q, and R are $10,000, $4,000, and $0; their case reserves are $9,000, $12,000, and $7,000. At April 30, cumulative paid amounts are $16,000, $4,000, and $2,000, and case reserves are $5,000, $8,000, and $6,000. Calculate total incurred loss at both dates and reconcile the change. Amounts are on a consistent basis with no separately included expenses or recoveries.
Method. At January 31, cumulative paid is:
January 31 case reserves total:
January 31 incurred loss is $14,000 + $28,000 = $42,000. At April 30, cumulative paid is:
April 30 case reserves total:
April 30 incurred loss is $22,000 + $19,000 = $41,000. Thus, paid increased by $22,000 - $14,000 = $8,000, while case reserves decreased by $19,000 - $28,000 = -$9,000. The net incurred change is $8,000 - $9,000 = -$1,000, which agrees with $41,000 - $42,000 = -$1,000.
The check is the reconciliation: the total increased paid amount does not prevent total incurred from declining when reserves fall by more. A common wrong calculation is to report the $8,000 paid increase as the incurred increase. The correction is to include the $9,000 reserve decrease as well.
Practical Checklist
Specify the claim population, coverage, valuation date, and treatment of expenses and recoveries.
Paid uses cumulative payments; case-incurred adds outstanding case reserves; ultimate includes estimated future loss for the defined population.
Use claim identifiers and aligned dates so payments and reserve snapshots refer to the same claims and valuation.
Show the paid, case-reserve, and any additional ultimate-estimate components separately, and check that no amount is omitted or counted twice.
The distinction matters in ratemaking because the chosen loss basis affects what the target represents. A paid basis reflects cash payments observed by the valuation date; a case-incurred basis also reflects current claim estimates; an ultimate basis is intended to represent the full expected cost for the defined population. A meaningful comparison requires the basis, valuation date, and scope to be consistent and documented. These definitions and reconciliation skills are aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus.
Check Your Understanding
For each problem, identify the requested basis and show the component reconciliation before checking the answer.
- A hypothetical insurer has three claims at December 31. Cumulative payments are $6,200, $0, and $3,800; case reserves are $1,800, $5,500, and $0. Find total paid and case-incurred loss. (Answer: Paid = $10,000; case-incurred = $17,300.)
- At March 31 a claim has cumulative paid loss of $14,000 and a case reserve of $11,000. At June 30, cumulative paid is $19,500 and the case reserve is $4,000. Find incurred loss at each date and its change. (Answer: March incurred = $25,000; June incurred = $23,500; change = -$1,500.)
- A reported claim has $22,000 paid, a $9,000 case reserve, and an estimated ultimate of $38,000. Find its incurred amount and estimated unpaid amount beyond paid. How much of that unpaid estimate exceeds the case reserve? (Answer: Incurred = $31,000; estimated unpaid = $16,000; amount beyond case reserve = $7,000.)
- A hypothetical portfolio has reported-claim paid loss of $40,000 and reported-claim ultimate estimates totaling $68,000. The estimate for claims not yet reported is $12,000. Find portfolio ultimate and the estimated unpaid amount on reported claims. State why the case reserves should not be added to the reported-claim ultimate again. (Answer: Portfolio ultimate = $80,000; reported-claim unpaid = $28,000; case reserves are already encompassed in the reported-claim ultimate estimates.)
- A data extract supplies $31,000 of cumulative paid loss at August 31, $7,000 of case reserves from a September 30 snapshot, and a $4,000 unreported-claim estimate at September 30. Can it reproduce September 30 case-incurred and portfolio ultimate loss? Identify the missing or mismatched information. (Answer: No. September 30 cumulative paid and September 30 case reserves on a consistent claim scope are needed for incurred; ultimate also requires a defined, reproducible estimate of all expected unpaid reported and unreported loss, not just the unreported amount.)