Introduction
An incurred-loss amount reflects both what has already been paid on a claim and what is still estimated to be owed. Claim status gives useful information about whether further payments are expected, but it does not by itself tell us how much loss the claim has incurred. In particular, a claim marked closed can still have positive incurred loss because its prior payments remain part of the total.
This distinction matters when loss information is organized into development triangles. A claim’s open or closed label describes its status at a particular valuation date; incurred loss combines the claim’s payments to that date with its outstanding case reserve at that same date. The examples below treat each claim record as a deterministic snapshot. They use no interest discounting, mortality assumption, or probability distribution: amounts are undiscounted dollars as recorded at the stated valuation date.
What Open and Closed Status Tell You
An open claim generally has some expected future activity or payment, so it may have a positive case reserve. That is not a guarantee: an open claim can have a zero reserve at a particular valuation date. A closed claim generally has no further payment expected under its current status, so its case reserve is commonly zero. But zero outstanding reserve does not mean zero incurred loss. The claim may already have generated payments.
Status is therefore not a substitute for the amounts in the incurred-loss calculation. It helps describe the claim’s state as of a date, while paid-to-date and case-reserve amounts determine its incurred amount. A claim that was open earlier may later be closed; when that happens, the earlier payments do not disappear. Similarly, if a claim’s status changes, the status label must be read at the relevant valuation date, not treated as a permanent property of the claim.
| Status at valuation | Paid to date | Case reserve | Incurred loss |
|---|---|---|---|
| Open | May be zero or positive | May be positive or zero | Paid to date plus case reserve |
| Closed | May be zero or positive | Typically zero | Prior payments plus any outstanding reserve recorded |
The word “typically” matters. A closed claim is usually recorded with no outstanding case reserve, but a data extract can contain exceptions, such as a status and reserve that have not yet been reconciled. The incurred amount is calculated from the reserve actually applicable at the valuation date; an inconsistent record should be investigated rather than silently changed. The status label alone does not authorize an analyst to replace a recorded reserve with zero.
Worked Example: A Closed Claim With Prior Payments
A hypothetical equipment insurer values one claim at December 31. The claim was open earlier in the year, received a payment of $4,800 in May and a payment of $3,700 in October, and is marked closed at December 31 with no outstanding case reserve. Find the claim’s incurred loss at that valuation date.
Method and assumptions. Use the claim-level incurred-loss definition. The two listed payments are all payments through December 31, the case reserve is zero at that date, and amounts are undiscounted. No interest rate, mortality assumption, or probability distribution is used.
First, add the cumulative payments: $$ P_i^{\text{paid}}(t)=\$4{,}800+\$3{,}700=\$8{,}500. $$
The claim is closed and its stated outstanding case reserve is \(C_i(t)=\$0\). Therefore: $$ I_i(t)=\$8{,}500+\$0=\$8{,}500. $$
Check. The incurred amount equals the total already paid because nothing remains in the case reserve. The common mistake is to assign zero incurred loss merely because the status is “closed.” That would discard $8,500 of prior payments; the correction is to retain those payments and add the zero reserve.
Why Payments and Reserves Are Added
The incurred-loss formula follows from separating the claim amount into two parts at the valuation date: the amount already paid and the amount still estimated to be outstanding. If those two parts are defined without overlap, together they represent the claim’s incurred amount on that basis. The reserve must therefore be an estimate of the remaining amount, not a restatement of the full amount including past payments.
For example, if $6,000 has already been paid and another $2,000 is reserved for future payment, the two components cover different portions of the claim: $6,000 paid and $2,000 outstanding. Adding them gives $8,000 incurred. If the $2,000 were instead a total estimate that already included the $6,000 paid, adding it to paid would count part of the claim twice. The meaning of the reserve field must therefore be understood before applying the formula.
The same identity can be applied claim by claim. When a set of claims is being summarized, the total incurred amount is the sum of each claim’s paid-to-date amount and case reserve. This does not change the definition: each claim contributes its payments plus its outstanding reserve at the same valuation date. The status label is useful for interpretation and data checks, but does not enter the addition as a separate dollar amount.
Worked Example: Open Claims With Different Payment Histories
A hypothetical commercial insurer reviews three claims at June 30. Claim A is open, with $4,200 paid and a $5,800 case reserve. Claim B is closed, with payments of $2,300 and $1,700 and no outstanding reserve. Claim C is open, with no payment yet and a $2,500 case reserve. Find the total paid, total case reserve, and total incurred amount for these claims.
Method and assumptions. Apply the claim-level definition at June 30 and then sum the components. The stated payments are cumulative through that date, all reserves are outstanding amounts excluding payments, and the amounts are undiscounted. No interest rate, mortality assumption, or probability distribution is used.
For Claim A: $$ P_A^{\text{paid}}=\$4{,}200,\qquad C_A=\$5{,}800,\qquad I_A=\$4{,}200+\$5{,}800=\$10{,}000. $$
For Claim B, first total the two payments: $$ P_B^{\text{paid}}=\$2{,}300+\$1{,}700=\$4{,}000. $$ Its reserve is zero, so \(I_B=\$4{,}000+\$0=\$4{,}000\).
For Claim C: $$ P_C^{\text{paid}}=\$0,\qquad C_C=\$2{,}500,\qquad I_C=\$0+\$2{,}500=\$2{,}500. $$
Now sum each component: $$ \text{total paid}=\$4{,}200+\$4{,}000+\$0=\$8{,}200, $$ $$ \text{total case reserve}=\$5{,}800+\$0+\$2{,}500=\$8{,}300, $$ $$ \text{total incurred}=\$8{,}200+\$8{,}300=\$16{,}500. $$
Check. Adding the three claim-level incurred amounts also gives \(\$10{,}000+\$4{,}000+\$2{,}500=\$16{,}500\). The open claims contribute both paid and reserved amounts where applicable; the closed claim contributes its $4,000 of prior payments. A common mistake is to count only reserves for open claims and omit payments on the closed claim.
Valuation Date and Claim Status Must Match
A claim’s paid amount, reserve, and status must all refer to the same valuation date. Mixing a year-end status with a reserve from an earlier extract can produce a misleading interpretation. The status may have changed between the two dates, and payments or reserve estimates may also have changed. When interpreting an incurred amount, identify the valuation date first, then read the status and financial fields as of that date.
A change in status does not itself determine the incurred amount. For instance, a claim can move from open to closed after settlement. Its case reserve may then become zero, while cumulative paid increases. The incurred amount at the later valuation is still calculated from the amounts recorded at that date. It is not recalculated as zero simply because the claim has closed.
Worked Example: Settlement Changes the Components, Not the Meaning
A hypothetical property claim is open at March 31 with $2,600 paid and a $4,400 case reserve. By June 30, the claim is settled and marked closed. Cumulative paid at June 30 is $6,900 and the case reserve is zero. Calculate incurred loss at both dates and compare the component changes.
Method and assumptions. Use the same claim-level incurred definition separately at each valuation date. Payments are cumulative through each date, reserves are outstanding amounts at the corresponding date, and the amounts are undiscounted. No interest rate, mortality assumption, or probability distribution is used.
At March 31: $$ I_i(\text{Mar 31})=\$2{,}600+\$4{,}400=\$7{,}000. $$
At June 30, the claim is closed, but its cumulative paid amount is $6,900: $$ I_i(\text{Jun 30})=\$6{,}900+\$0=\$6{,}900. $$
The paid amount increased by \(\$6{,}900-\$2{,}600=\$4{,}300\), while the case reserve decreased by \(\$0-\$4{,}400=-\$4{,}400\). Combining those component changes gives: $$ \$4{,}300+(-\$4{,}400)=-\$100, $$ which matches the change in incurred amount, \(\$6{,}900-\$7{,}000=-\$100\).
Check. The arithmetic reconciles at both dates and across the change. The closed claim has $6,900 incurred, not zero. The example also shows why status alone cannot tell us whether the incurred amount rose or fell; the payment and reserve amounts are needed.
Common Mistakes and Data Checks
- Setting incurred loss to zero for a closed claim. Closed status generally means no outstanding reserve; it does not reverse or erase paid-to-date amounts.
- Adding a total estimate to payments. Confirm that the reserve is outstanding only. If a field is already a total estimate including prior payments, adding it to paid would double-count.
- Ignoring an open claim with no payments. An open claim with zero paid and a positive case reserve still has positive incurred loss.
- Assuming every open claim has a positive reserve. Status and reserve are distinct fields. A zero reserve on an open claim may be valid or may merit review, but it is not automatically a positive amount.
- Combining values from different dates. Paid amount, case reserve, and status should be aligned to one valuation date before interpreting the result.
These distinctions support reliable interpretation of incurred-loss information and are aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus. In practice, they also provide a useful first check: does the stated incurred amount equal paid-to-date plus the case reserve on a consistent date and basis?
Check Your Understanding
For each hypothetical claim record, use the stated valuation date and report the requested amount. Amounts are undiscounted; no interest, mortality, or probability model is used.
- A closed claim has payments of $3,150 and $4,850 through September 30 and a zero case reserve. What is its incurred loss? (Answer: $8,000)
- An open claim has $5,600 paid and a $3,400 outstanding case reserve at December 31. Calculate its incurred loss, and identify how much is still outstanding. (Answer: incurred loss $9,000; outstanding reserve $3,400)
- At June 30, Claim A is open with $2,700 paid and a $6,300 reserve. Claim B is closed with $11,400 paid and a zero reserve. Find total paid, total reserve, and total incurred for the two claims. (Answer: total paid $14,100; total reserve $6,300; total incurred $20,400)
- An open claim has $2,000 paid and a $5,000 reserve at March 31. At June 30 it has $4,500 paid and a $2,500 reserve. Calculate incurred loss at each date and the change. (Answer: $7,000 at both dates; change $0)
- A portfolio snapshot contains three claims: an open claim with $1,800 paid and $4,200 reserved; a closed claim with $6,500 paid and zero reserved; and an open claim with $900 paid and $2,100 reserved. Calculate total paid, total case reserve, and total incurred. (Answer: total paid $9,200; total case reserve $6,300; total incurred $15,500)