Why Reconcile Claim Inventories and Triangles?
A claim inventory gives claim-level detail at a point in time; a development triangle summarizes amounts by period and development age. These views should be consistent when they use the same valuation date, claim population, accounting basis, and coverage of amounts. When totals differ, the difference is a diagnostic: it may reveal a cutoff mismatch, a coding problem, an omitted claim, or simply a difference in what each data source includes.
The aim is not to make two totals agree by applying an unexplained plug. It is to identify the specific adjustments that make the comparison like-for-like, quantify each adjustment, and retain any residual difference for investigation. This is especially important when claim-level case reserves are compared with aggregate triangle amounts: a claim inventory usually describes reported claims, while an aggregate incurred total may contain amounts that are not assigned to individual claims.
Set the Basis Before Comparing Amounts
Start by writing down exactly what the triangle cell represents. For example, a paid-loss triangle cell might contain cumulative indemnity payments for claims from one accident year, recorded through a particular valuation date. An incurred-loss cell might contain those paid losses plus case reserves on the same basis. A claim-level inventory may instead include adjustment expenses, recoveries, transactions posted after the triangle cutoff, or claims assigned to a different origin period.
For a matched set of reported claims, let \(P_i\) be claim \(i\)'s cumulative paid loss as of the valuation date and let \(C_i\) be its case reserve on the same loss basis and date. Then the inventory's reported-claim paid and incurred amounts are:
This identity is an accounting reconciliation, not a development method. It applies only when paid amounts and case reserves have compatible scope and timing. If, for example, paid is net of recoveries but case reserves are gross, adding them does not produce either a fully gross or a fully net incurred amount without a further adjustment.
A triangle can include amounts not present in the claim inventory, such as a separately held bulk amount, or can differ because the inventory extract omits some claims. Therefore, equality between reported-claim incurred and a triangle's incurred cell is not automatic. The comparison should distinguish a mismatch within the data from a legitimate difference in population or reserve scope.
A Reconciliation Sequence
Specify the date and whether transactions are selected by accounting posting date, transaction effective date, or another defined convention. Apply the triangle's convention to the inventory.
Check the accident, policy, or report period used by the cell. Look for claims missing from the extract, duplicate claim records, and claims assigned to a different period.
Determine whether the comparison is for loss only or includes adjustment expense, and whether paid and case amounts are gross or net of recoveries.
Show the inventory starting amount, each supported adjustment, and the resulting amount. Compare that result with the triangle and investigate any residual.
The sequence matters: an apparent amount discrepancy can be caused by records belonging to different cells, not by an arithmetic error. Keep adjustments separate rather than combining them into one net figure; a positive timing adjustment and a negative coding adjustment can otherwise conceal each other.
Worked Example: Aligning a Transaction Cutoff
A hypothetical insurer is reconciling reported loss for one accident year at March 31. Its triangle uses payments posted on or before March 31 and case reserves at that date. The inventory extract was run on April 5. It shows three claims: Claim A has $10,000 paid through March 31 and a $6,000 case reserve; Claim B has $4,000 paid and no case reserve; Claim C has $3,000 paid, posted on April 2, and a $5,000 case reserve as of March 31. The triangle's paid-loss cell is $14,000 and its reported-claim case reserves total $11,000. Reconcile the inventory to the triangle basis.
Method: transaction-cutoff adjustment. Claim A and Claim B payments were posted by the cutoff, so both remain in the comparison. Claim C's $3,000 payment was posted after March 31. Because the triangle uses posting date, exclude that payment from the inventory's paid total. Do not remove Claim C's March 31 case reserve: it is an as-of-date reserve, not an after-cutoff payment.
The raw extract's paid total is \(10{,}000+4{,}000+3{,}000=\$17{,}000\). The cutoff adjustment is \(-\$3{,}000\), giving adjusted paid of \(\$17{,}000-\$3{,}000=\$14{,}000\). The case reserve total is \(6{,}000+0+5{,}000=\$11{,}000\). Thus adjusted reported-claim incurred is \(\$14{,}000+\$11{,}000=\$25{,}000\).
The triangle figures imply incurred of \(\$14{,}000+\$11{,}000=\$25{,}000\), so the adjusted inventory agrees on both paid and case reserve totals. The common mistake avoided is including the April 2 payment merely because the claim itself was reported by March 31. The cutoff applies to transactions as well as to claim records.
Gross and Net Amounts Must Be Labeled Correctly
A recovery recorded as a negative payment reduces paid on a net basis. To compare that amount with a gross-paid triangle, add the recovery back, provided the recovery amount is known and the triangle's gross basis is confirmed. State the basis of case reserves separately; they are not automatically on the same basis as paid amounts.
Worked Example: Correcting a Net-of-Recoveries Inventory
A hypothetical claim inventory reports paid of $125,000, including a $5,000 recovery recorded as a negative payment. It also reports $35,000 of case reserves, which are confirmed to be gross of recoveries. The corresponding gross triangle cell contains $132,000 paid and $38,000 of case reserves. Reconcile the inventory to the gross triangle and explain the difference.
Method: gross-up followed by a scope bridge. Since the inventory's paid amount includes the recovery as a negative payment, $125,000 is net of that recovery, not gross. Gross paid is \(\$125{,}000+\$5{,}000=\$130{,}000\). The inventory's gross case reserves remain $35,000, as specified. Its gross incurred amount is therefore \(\$130{,}000+\$35{,}000=\$165{,}000\).
Compare the gross inventory with the triangle: paid differs by \(\$132{,}000-\$130{,}000=\$2{,}000\), and case reserves differ by \(\$38{,}000-\$35{,}000=\$3{,}000\). Suppose claim-level investigation finds one omitted in-scope claim with $2,000 paid and a $3,000 case reserve. Adding that claim gives gross paid of \(\$130{,}000+\$2{,}000=\$132{,}000\), case reserves of \(\$35{,}000+\$3{,}000=\$38{,}000\), and incurred of \(\$132{,}000+\$38{,}000=\$170{,}000\).
The adjusted inventory now agrees with the gross triangle. The common mistake avoided is calling the $125,000 starting amount gross because it appears as a positive total. A negative recovery within that total makes it net of recoveries; the paid and case-reserve bases must each be identified before incurred is calculated.
Scope and Coding Differences
A reconciliation can fail even when the valuation cutoff is correct. A claim may be assigned to the wrong accident year, or the inventory and triangle may use different definitions of loss and adjustment expense. ALAE and ULAE are not interchangeable with indemnity loss. If the triangle is loss-only, an inventory total that includes allocated adjustment expense must be separated before comparison. Likewise, an amount should not be shifted between origin-period cells merely to force a match: investigate the underlying claim coding and use the triangle's stated period definition.
Worked Example: Separating Scope and Correcting Period Coding
A hypothetical insurer compares an inventory labelled accident year 2024 with a loss-only triangle cell for accident year 2024, valued at December 31. The inventory shows $82,000 of paid loss, $17,000 of case loss, $5,000 of paid ALAE, and $2,000 of ALAE case reserves. The triangle shows $80,000 paid loss and $20,000 case loss reserves. Review establishes that the $82,000 paid-loss figure includes a $4,000 payment posted after the cutoff and a $6,000 payment for an accident-year 2023 claim coded as 2024. The inventory also omitted an accident-year 2024 claim with $8,000 paid loss and a $3,000 case reserve. Reconcile the loss-only amounts.
Method: scope separation and claim-level coding bridge. First exclude ALAE because the triangle cell is loss-only. The $5,000 paid ALAE and $2,000 ALAE case reserve do not enter this comparison. Next apply the identified paid adjustments: remove the $4,000 after-cutoff transaction, remove the $6,000 belonging to accident year 2023, and add the omitted accident-year 2024 claim's $8,000 paid loss.
Adjusted paid loss is \(\$82{,}000-\$4{,}000-\$6{,}000+\$8{,}000=\$80{,}000\). The inventory's $17,000 case loss reserves exclude ALAE already, so add the omitted claim's $3,000 case reserve: \(\$17{,}000+\$3{,}000=\$20{,}000\). Reconciled loss incurred is \(\$80{,}000+\$20{,}000=\$100{,}000\), equal to the triangle's implied incurred loss of \(\$80{,}000+\$20{,}000=\$100{,}000\).
The common mistake avoided is comparing the inventory's all-in paid and reserve totals directly with a loss-only triangle. The period-coding adjustment also matters: the $6,000 payment belongs in the 2023 cell, not the 2024 cell. Each adjustment is supported by the claim-level records and has a stated direction.
Why the Additive Check Works—and When It Does Not
For each claim on a consistent basis, incurred is defined as paid plus case reserve. Summing that definition over the same set of claims gives the reconciliation identity:
This follows from distributing a finite sum over addition: each claim's paid amount appears once in the paid total, and each claim's case reserve appears once in the reserve total. Therefore, when the population, cutoff, and measurement basis match, a difference in incurred must be traceable to a difference in paid, case reserves, or both.
The identity does not establish that an aggregate incurred triangle cell contains only those claim-level amounts. If the cell includes an additional aggregate provision or a different population, the comparison requires that item to be identified separately. Nor does the identity justify adding gross paid to net case reserves, mixing currencies, or adding ALAE to a loss-only cell. In those cases, the terms do not represent a common basis.
Common Reconciliation Traps
- Using two different cutoff conventions. A claim may be in both data sets while a payment is included in only one. Check transaction dates and the stated valuation rule.
- Calling net paid gross. If recoveries reduce recorded paid, identify the net basis and gross up only when the recovery amount and target basis are known.
- Comparing different scopes. Separate loss from ALAE or ULAE when the triangle does not include those expenses.
- Ignoring claim-period coding. A claim assigned to the wrong origin period affects more than one triangle cell. Correct the assignment from the underlying record rather than netting the difference elsewhere.
- Treating a residual as an adjustment. An unexplained difference is not a reconciliation. Report it as unresolved and identify the additional evidence needed.
A useful reconciliation schedule shows, for each adjustment, its reason, amount, sign, and evidence source. That schedule makes it possible to distinguish a supported correction from a judgmental change and to reproduce the result at a later valuation.
Check Your Understanding
For each problem, reconcile only the amounts on the stated common basis. Assume all dollar amounts are exact.
- A matched claim inventory has $46,000 paid and $12,000 case reserves. Investigation finds an omitted in-scope claim with $3,000 paid and a $2,000 case reserve. What are reconciled paid and incurred? (Answer: paid $49,000; incurred $63,000.)
- An inventory reports net paid of $91,000, including a $4,000 recovery as a negative payment, and gross case reserves of $22,000. What are gross paid and gross incurred? (Answer: gross paid $95,000; gross incurred $117,000.)
- An inventory shows $58,000 paid and $17,000 case reserves. Of the paid amount, $5,000 was posted after the triangle's cutoff; all case reserves are as of that cutoff. What are cutoff-aligned paid and incurred? (Answer: paid $53,000; incurred $70,000.)
- A loss-only triangle is compared with an inventory showing $40,000 paid loss, $10,000 case loss reserves, $6,000 paid ALAE, and $2,000 ALAE case reserves. Assuming no other differences, what loss-only paid and incurred amounts should be compared? (Answer: paid loss $40,000; incurred loss $50,000.)
- An inventory's $70,000 paid loss includes $9,000 for a claim correctly belonging to the prior accident year. A separate in-scope claim omitted from the inventory has $4,000 paid and $3,000 case reserves. The inventory has $15,000 case reserves, and no other differences exist. What are reconciled paid and incurred for the current accident year? (Answer: paid $65,000; case reserves $18,000; incurred $83,000.)