Why Claim Status Must Be Measured Carefully
A paid-loss adjustment for settlement speed depends on comparing paid losses with the right measure of claim closure. The data can be deceptive: a claim may make partial payments while open, close with no payment, reopen after a closure, and later close again. Counting payment transactions or closure events as if each were a separate settled claim can distort the settlement rate and therefore the adjusted paid amount.
The key is to define the unit and the valuation date first. For a given reported-claim cohort, each claim contributes once to the claim count. Its status is then read as of a specified valuation date. A historical closure event is not, by itself, evidence that the claim is currently closed.
This is a settlement-speed adjustment: it scales paid loss by the ratio of standard to observed settlement rates. It does not change the underlying payment records, and it does not by itself correct a change in the severity of claims that have been paid. The selected standard rate must correspond to the same basis and development age as the observed rate.
Build a Status Snapshot Before Calculating
A reliable calculation starts from one row per claim, rather than one row per payment or closure event. At the valuation date, identify the claim's current status and its cumulative paid amount. A useful status table separates three ideas:
- Claim count: each reported claim appears once in \(N\), regardless of the number of transactions or status changes.
- Current closure status: a claim counts in \(C\) if it meets the selected definition of closed at the valuation date. A claim that has reopened is not currently closed.
- Cumulative paid loss: include payments made through the valuation date, whether the claim is currently open or closed. A closed claim with no payment contributes zero dollars to \(P\), not a missing value.
A closed-without-payment claim generally counts as closed when the operational definition is “claim closed,” even though its paid amount is zero. That treatment is appropriate only if the standard settlement rate was constructed using the same convention. If a data system instead defines settlement as a closure with an indemnity payment, both the observed rate and standard rate must use that narrower definition. Mixing the two conventions makes the adjustment internally inconsistent.
Partial payments do not make an open claim closed. They do contribute to cumulative paid loss. Likewise, multiple closure events do not create multiple claims: count the claim once if it is currently closed, and zero times if it is currently open. This snapshot approach avoids treating a reopened claim as permanently settled simply because it was closed at some earlier time.
Worked Example: Reopened Claims and the Current Closure Count
A hypothetical cohort contains 14 reported claims. There have been 11 closure events. Two claims that had closed have since reopened; the other nine claims associated with closure events are distinct and are currently closed. The remaining three claims have never closed. Cumulative paid loss is $42,000, and the standard settlement rate is 0.60. Find the adjusted paid loss using current status.
Method: take a valuation-date snapshot. The 11 closure events are not 11 currently closed claims. The two reopened claims are currently open, while the other nine are currently closed. Thus \(N=14\) and \(C=9\).
The observed settlement rate is $$ q=\frac{C}{N}=\frac{9}{14}=0.642857\ldots $$
Apply the standard-to-observed rate ratio: $$ P_{\text{adj}}=\$42{,}000\frac{0.60}{9/14} =\$42{,}000\left(\frac{0.60\times14}{9}\right) =\$42{,}000\left(\frac{14}{15}\right) =\$39{,}200. $$
Check: The observed rate, about 0.6429, exceeds the standard rate of 0.60, so the adjustment factor must be below 1. The result, $39,200, is below $42,000, as expected. The common mistake is to use all 11 closure events as the numerator; the rate is based on claims currently closed, not events.
Why the Adjustment Uses a Rate Ratio
The adjustment formula follows from a proportional model for paid loss at a fixed development age. Suppose the paid amount per reported claim can be represented as the settlement rate multiplied by a standardized paid amount per settled claim, \(m\). In this working model, \(P/N=q\,m\), so paid loss is proportional to the observed settlement rate when \(m\) is held constant. At the standard rate, the corresponding amount per reported claim is \(q_s m\).
The ratio of the standard-basis amount to the observed amount per reported claim is therefore $$ \frac{q_s m}{q m}=\frac{q_s}{q}. $$ Multiplying the observed paid loss by this ratio gives $$ P_{\text{adj}}=P\frac{q_s}{q}. $$
This derivation explains both the direction and the limitation of the adjustment. When \(q_s>q\), the standard basis has a higher settlement rate and the adjusted paid amount increases. When \(q_s<q\), it decreases. The calculation assumes that differences in the paid amount are appropriately represented by settlement-rate differences; if paid severity or the pattern of partial payments changes independently, the simple rate ratio may not isolate settlement speed.
Partial Payments, No-Payment Closures, and Repeat Events
The claim-status count and paid-loss total answer different questions. The count records how many claims meet the closure definition at the valuation date. The paid total records dollars paid on all claims through that date. Therefore, the claim-level reconciliation should not require every dollar in \(P\) to come from claims counted in \(C\): open claims can already have partial payments.
A practical control is to compare the status snapshot with the transaction history. For each claim, verify that the cumulative paid amount includes all valid payments through the valuation date, while the closure indicator reflects the latest valid status. Reopenings should reverse the current closed status where the data definition says the claim is open again; they should not erase prior payments. A later closure changes the status snapshot again, but still adds no second claim to the denominator.
| Claim history at valuation | Count in \(N\) | Count in \(C\) | Contribution to \(P\) |
|---|---|---|---|
| Open, with partial payments | One | Zero | Include payments made |
| Currently closed, with payments | One | One | Include payments made |
| Currently closed, no payment | One | One under a general closure definition | Zero |
| Previously closed, now reopened | One | Zero | Include payments made |
| Closed, reopened, and closed again; currently closed | One | One | Include payments made |
Worked Example: Partial Payments and No-Payment Closures
A hypothetical cohort has 24 reported claims. At valuation, 10 are currently closed, including two closed with no payment. Four other claims have each closed in the past but are now reopened; the remaining claims are open and have never closed. Some open claims have partial payments. Cumulative paid loss across all 24 claims is $72,000. The standard settlement rate is 0.50. Calculate the adjusted paid loss.
Method: count current status, then use all cumulative paid loss. The four reopened claims are currently open, so they do not count in \(C\). The two no-payment closures do count because the stated status definition includes all closed claims. Thus \(C=10\), \(N=24\), and $$ q=\frac{10}{24}=\frac{5}{12}=0.416667\ldots $$
The partial payments on open claims remain in the $72,000 cumulative paid total. Do not remove them simply because those claims are not counted as currently closed. The adjustment is $$ P_{\text{adj}}=\$72{,}000\frac{0.50}{5/12} =\$72{,}000(1.20) =\$86{,}400. $$
Check: The standard rate of 0.50 is greater than the observed rate of about 0.4167, so the adjustment factor is greater than 1. The result is therefore higher than the observed paid loss. A common error is either to exclude the two no-payment closures from the count without changing the standard-rate basis, or to omit partial payments on open claims from \(P\).
Adjust Cohorts Separately When Standards Differ
If cohorts have different standard rates or different development ages, calculate each adjustment on its own matching basis before combining adjusted amounts. Applying one pooled rate ratio can hide differences in settlement patterns and paid-loss weights. The following example uses two hypothetical cohorts with separate standard rates.
Worked Example: Combining Adjustments Across Two Cohorts
At a valuation date, Cohort A has 40 reported claims, 18 currently closed, cumulative paid loss of $135,000, and a standard settlement rate of 0.60. One of its currently closed claims has no payment; three other claims have reopened and are currently open. Cohort B has 25 reported claims, 15 currently closed, cumulative paid loss of $75,000, and a standard rate of 0.50. Three of Cohort B's currently closed claims have no payment, and two previously closed claims are now open. Find the adjusted paid loss for each cohort and in total.
Cohort A. Current closed status gives \(C_A=18\), so $$ q_A=\frac{18}{40}=0.45,\qquad P_{\text{adj},A}=\$135{,}000\frac{0.60}{0.45} =\$135{,}000\left(\frac{4}{3}\right) =\$180{,}000. $$
Cohort B. The three no-payment claims are included among the 15 currently closed claims; the two reopened claims are not. Therefore, $$ q_B=\frac{15}{25}=0.60,\qquad P_{\text{adj},B}=\$75{,}000\frac{0.50}{0.60} =\$75{,}000\left(\frac{5}{6}\right) =\$62{,}500. $$
Add the cohort-level adjusted amounts: $$ P_{\text{adj,total}}=\$180{,}000+\$62{,}500=\$242{,}500. $$
Check: Cohort A is adjusted upward because 0.60 exceeds 0.45. Cohort B is adjusted downward because 0.50 is below 0.60. The combined adjusted amount, $242,500, is between the two possible extremes and exceeds the unadjusted total of $210,000 because Cohort A's upward adjustment is larger than Cohort B's reduction. Do not average the two standard rates and apply that average to total paid loss; the cohorts have different observed rates and paid amounts.
Implementation Checks and Limitations
Use a consistent reported-claim population and an explicit valuation date for both the status count and paid total.
Use the latest valid status. A reopened claim is currently open unless it has subsequently closed again.
Sum valid cumulative payments through valuation, including payments on open claims; retain zero as the paid amount for a no-payment claim.
Confirm that observed and standard rates use the same treatment of no-payment closures, reopenings, claim eligibility, and development age.
Compute \(q=C/N\), apply \(q_s/q\), and check whether the direction of change agrees with the comparison of \(q_s\) and \(q\).
The formula is undefined when \(q=0\), because there is no observed closed-claim rate to use as a denominator. It should not be made finite by inserting an arbitrary small rate; use another method or a justified estimate instead. Very small \(q\) can also produce a highly sensitive adjustment, so the result should be reviewed for data quality and appropriateness.
Another limitation is that a scalar closure-rate adjustment can combine effects that the rate alone cannot distinguish. For example, a cohort may have a different mix of claim sizes, different payment timing on open claims, or different paid severity among closed claims. The settlement-rate adjustment is most interpretable when those features are sufficiently comparable or are addressed separately. It is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus as a method for controlling paid-loss distortions associated with changing settlement rates, not as a substitute for checking the underlying claim data.
- Do not count events as claims. A claim with several closure events still contributes at most one to \(C\).
- Do not equate payment with closure. An open claim can have paid loss, and a closed claim can have none.
- Do not mix definitions. The standard and observed rates must count the same kinds of closures.
- Do not pool incompatible standards. Adjust distinct cohorts with their own standard rates before adding results.
Check Your Understanding
For each hypothetical problem, use current status rather than historical closure-event counts. Assume every stated standard rate uses the same closure definition as the observed rate.
- A cohort has 32 reported claims, 12 currently closed, cumulative paid loss of $48,000, and a standard rate of 0.375. Find the adjusted paid loss. (Answer: $48,000)
- A cohort has 18 reported claims, 6 currently closed, including one closed with no payment. Cumulative paid loss is $30,000 and the standard rate is 0.50. Find the adjusted paid loss. (Answer: $45,000)
- A cohort has 20 reported claims and 10 closure events. Three claims that had closed are now reopened, while the other seven claims associated with closure events are currently closed. Cumulative paid loss is $56,000 and the standard rate is 0.35. Find the adjusted paid loss. (Answer: $56,000)
- Cohort A has 50 reported claims, 20 currently closed, $100,000 paid, and a 0.50 standard rate. Cohort B has 30 reported claims, 18 currently closed, $72,000 paid, and a 0.40 standard rate. Adjust each cohort separately and find the total. (Answer: $173,000)
- A cohort has 40 reported claims, 8 currently closed (including 2 closed with no payment), $64,000 cumulative paid loss, and a standard rate of 0.30. Some open claims have partial payments. Find the adjusted paid loss. (Answer: $96,000)