Why a Claim-Severity Task Needs a Precise Target
A claim-severity prediction estimates a numeric cost for an individual claim. That description is not yet a usable task. “Predict claim cost” could mean the next three months of payments on an open claim, all future payments until closure, or the claim’s total cost including amounts already paid. Those outcomes differ, even when they refer to the same claim.
For an actuarial use, define the population, the point at which the prediction is made, and the future cost being predicted. Also state the measurement basis and intended use. A clearly framed target can support a reserving estimate or help prioritize claims for review; it does not, by itself, specify a model or dictate an action. This framing is aligned with the SOA Exam PA (Predictive Analytics) syllabus.
Five Choices That Define the Task
The choices below form one connected specification. Changing one can change the outcome being predicted, even if the model and claim records remain unchanged.
- Claim population and prediction unit. State which claims qualify at the prediction time—for example, reported, open property claims—and what one prediction represents. A policy, claimant, or accident is not automatically interchangeable with a claim. If a policy can have several claims, say whether each claim receives a separate prediction.
- Prediction time. Set the date or event at which the prediction is to be available. For a recurring process, specify when a claim becomes eligible for a new prediction. The intended use depends on having the prediction in time to inform it.
- Future cost and period. Define the cost after the prediction time. A fixed horizon, such as the next 90 days, is different from all remaining cost until closure. If the target is total cost over a period, say whether it includes amounts paid before that period; normally a target described as future cost excludes them.
- Measurement basis and units. Specify paid or incurred amounts, gross or net of recoveries, included cost components, currency, and whether amounts are nominal or adjusted to a stated price basis. Use one consistent unit, such as dollars per claim.
- Intended use. State whether the predictions support a portfolio’s future-payment estimate, claim review prioritization, or another stated purpose. This helps determine which horizon and cost definition are relevant. A prediction describes an outcome; deciding what action to take is a separate step.
A short task statement can capture these decisions: “For each reported, open equipment claim at the start of each month, predict the gross indemnity payments in dollars expected during the following 90 days, to support a near-term payment estimate.” It identifies a population, prediction timing, target, units, and purpose. It does not claim to predict all eventual claim cost.
Future Cost Is Not the Same as Total Cost
Suppose a claim has already generated payments before the prediction date. If the task is to predict future payments, those past payments are not part of the target. They may be useful context for a prediction, but they are not future outcomes. Conversely, a task explicitly defined as ultimate total paid cost could include both past and future payments. The label must match the intended question.
For a fixed future period, the target can be defined from dated payment transactions. Let \(t_0\) be the prediction time and \(H\) the horizon length. If \(p_{ij}\) is the amount of payment \(j\) on claim \(i\), and \(t_{ij}\) is its payment date, the future paid target is the sum of payment amounts occurring after \(t_0\) and through \(t_0+H\). For this definition, payment dates at the endpoint are included.
Here \(\mathbf{1}\{\cdot\}\) equals 1 when the condition in braces is true and 0 otherwise. This formula defines a paid-cost target; it does not include case estimates or unpaid obligations unless the task defines a different target. For net cost, define which recoveries or other offsets are subtracted. For incurred cost, specify the valuation convention rather than treating it as a payment total.
Worked Example: Defining a 90-Day Payment Target
A hypothetical insurer wants a near-term payment estimate for property claims. At the start of April 1, 2026, it considers reported claims that are still open. One eligible claim has $4,500 paid before that date. During the next 90 days, payments are $1,200 on April 12, $800 on May 20, and $500 on June 30. Define the claim’s target and calculate its realized value.
Method. Treat each open claim as one prediction unit. Set \(t_0\) to the start of April 1 and \(H\) to 90 days, ending June 30. Define the outcome as gross indemnity payments after \(t_0\) through June 30, in nominal dollars. This is appropriate to the stated near-term payment purpose.
All three listed payments occur after April 1 and on or before June 30, so each is included. The calculation is:
The $4,500 paid before April 1 is excluded. The realized target is $2,500 per claim. Check: adding the four payments would give $7,000, but that would mix past cost with the defined future-payment target. The common mistake is to call that combined amount the next-90-day outcome.
Choosing the Cost Basis for the Purpose
“Cost” needs a measurement convention. Paid amounts refer to payments made in the defined period. Incurred amounts follow the specified incurred-cost convention and may include amounts that are not yet paid. Gross cost is measured before specified recoveries; net cost subtracts the recoveries included by definition. These are different targets, not interchangeable labels.
| Framing choice | Example specification | Question answered |
|---|---|---|
| Paid or incurred | Payments made in the next 90 days | How much cash is paid in the horizon? |
| Gross or net | Gross indemnity, before salvage recoveries | Which offsets, if any, reduce the target? |
| Cost components | Indemnity only; allocated expenses excluded | Which types of claim cost are counted? |
| Currency and price basis | Nominal U.S. dollars | How are amounts expressed and compared? |
| Future period | From the prediction time through the next 90 days | When must the cost occur to count? |
A reserving use may require predictions of future payments over a defined horizon or remaining future cost; the task statement should say which. A review use may instead require a consistent severity measure to rank claims. In either case, a prediction is not automatically a reserve for every purpose, and a high predicted cost alone does not establish that a claim should receive a particular action.
Worked Example: Net Cost Through Claim Closure
A hypothetical motor insurer wants to estimate remaining net indemnity payments on open claims at a valuation date of January 1, 2026. For one claim, the future gross indemnity payments before closure are $3,250, $1,100, and $700. A $300 recovery is also received after the valuation date. Indemnity payments before January 1 total $2,000. The task excludes expenses. Define and calculate the target.
Method. Use one open claim as the prediction unit, set the prediction time to January 1, and define the outcome as all remaining gross indemnity payments less recoveries received after that date, in dollars, through closure. This is a remaining-net-cost target, not a next-period cash-flow target.
First sum the future gross payments:
Then subtract the included future recovery:
The target is $4,750 per claim. The $2,000 paid before the valuation date is excluded because the task concerns remaining cost. Check: the result is $300 less than future gross payments, as required by the net definition. The common mistake is to add the past $2,000 and report $6,750, which answers a different question.
From Individual Severity Predictions to a Reserving Estimate
If the intended use is a future-payment estimate for a defined set of claims, the claim-level predictions can be added when they refer to the same cost definition and horizon. Let \(C_i\) denote claim \(i\)’s future cost, and let \(\mathcal{I}\) denote the information available for the claim set at prediction time. If each prediction is the conditional expected cost \(E[C_i\mid\mathcal{I}]\), then the expected total is the sum of those predictions, provided the costs have finite expectations.
Why this holds. Conditional expectation is linear. For two claims, \(E[C_1+C_2\mid\mathcal{I}]=E[C_1\mid\mathcal{I}]+E[C_2\mid\mathcal{I}]\). Applying the same addition repeatedly gives the result for \(n\) claims. No independence assumption is needed. However, every \(C_i\) must represent the intended target: adding predictions for different horizons or incompatible cost bases does not produce the expected total for one coherent cost measure.
This result explains one connection between claim-level severity and a portfolio estimate. It does not make a limited-horizon payment estimate equal to all remaining liability, nor does it settle what cost definition a particular reserving process requires. Those are framing choices that must be made first.
Worked Example: Prioritizing Claims for Review
A hypothetical equipment insurer reviews open claims at the start of January 1, 2026. It wants each claim’s predicted gross indemnity payments over the following six months, in nominal dollars, to prioritize two of four claims for manual review. A model has produced predictions and the subsequently observed six-month outcomes below. Calculate which claims are selected and compare their predicted and realized total costs.
| Claim | Predicted six-month cost | Realized six-month cost |
|---|---|---|
| A | $18,200 | $21,000 |
| B | $7,600 | $6,900 |
| C | $24,500 | $19,000 |
| D | $12,000 | $15,500 |
Method. The prediction unit is one open claim. The prediction time is January 1, the outcome is gross indemnity paid in the next six months, and the use is ranking claims for a two-claim review capacity. Rank by predicted cost from highest to lowest: C ($24,500), A ($18,200), D ($12,000), and B ($7,600). Therefore, select C and A.
Their predicted total is:
Their realized total is:
The selected pair’s predicted total exceeds its realized total by $2,700. Check: \( \$42{,}700-\$40{,}000=\$2{,}700 \). This difference describes prediction performance for the selected pair; it does not mean review caused a change in cost. The common mistake is to treat the ranking as a recommendation that review will reduce severity. The task predicts cost to prioritize attention; the effect of any action is a separate question.
A Practical Framing Check
Before building a claim-severity prediction, write a one-sentence target specification and check each part against the intended use:
State whether one row and one prediction represent one claim, rather than leaving policy, claimant, and claim ambiguous.
Describe which claims qualify and when the prediction is to be made.
Specify the period, payment or incurred basis, gross or net convention, included cost components, and treatment of costs before the prediction time.
Give the currency and price basis, then say whether the prediction supports a future-payment estimate, review prioritization, or another defined purpose.
An answer that says only “predict severity” leaves too much open to interpretation. A precise statement lets a reader determine what one prediction means and what observed outcome would count as correct. It also helps prevent a sound prediction from being used as if it answered a different actuarial question.
Check Your Understanding
For each problem, state the relevant target or calculation. Assume all stated amounts are in dollars.
- A hypothetical insurer predicts payments for open glass claims at the start of July 1. A claim had $250 paid before that date and then receives payments of $300 on July 10 and $450 on September 29. The target is gross payments in the next 90 days, including the endpoint. What is the realized target, and is the earlier payment included? (Answer: $750; the earlier $250 is excluded.)
- For a hypothetical open liability claim, the target is remaining net indemnity through closure from the valuation date. Future payments are $6,000 and $2,500; a future recovery is $500; prior payments are $3,000. What is the target? (Answer: $8,000.)
- A hypothetical review process predicts next-quarter gross payments for each open claim, in nominal dollars. The predictions for claims P, Q, and R are $9,200, $14,000, and $11,500; capacity permits review of two claims. Which claims are prioritized, and what is their combined predicted cost? (Answer: Q and R; $25,500.)
- A hypothetical reserving task predicts future paid indemnity for each open claim over the next six months. Two claims have conditional expected costs of $4,800 and $7,250 under the same target. What is the expected total for the pair, and is independence required for this sum? (Answer: $12,050; independence is not required.)
- A hypothetical property claim has $1,100 paid before the prediction date. During the specified future 30-day horizon, gross indemnity payments are $900 and $600, and a $200 recovery is received. The target is net indemnity in the 30-day horizon. What is the target, and why is the $1,100 excluded? (Answer: $1,300; the prior payment is outside the defined future horizon.)