Using Expert Judgment in Capital Models

Why Expert Judgment Needs Structure

Capital models often require assumptions that cannot be estimated reliably from the available observations alone. A new exposure, changing operating practice, rare event, or short history may leave actuaries with limited data about event rates or loss severity. People with relevant operational, underwriting, claims, engineering, or finance experience may know something the data do not yet show. That knowledge can improve a model, but only when it is elicited and used transparently.

Expert judgment is not a substitute for a defined model question. Before asking for an estimate, specify the risk being modeled, the loss basis, the time horizon, the exposure unit, and the parameter required. For example, “How many events?” is incomplete unless the event definition, population, and period are clear. A rate per location-year is not interchangeable with a rate per policy-year.

Definition: Expert judgment is a reasoned assessment provided by people with relevant knowledge and used to inform a model assumption or parameter. A structured judgment records the question, evidence, elicitation method, estimate, rationale, limitations, and approval. An unsupported management overlay is an adjustment to a model result or assumption that lacks a clearly stated basis, reproducible calculation, or adequate documentation.

Judgment can inform an event rate, a severity assumption, or a parameter such as a trend factor. It can also identify a model feature that does not represent current practice. These uses should be distinguished. An estimate of a parameter within the existing model is not the same as changing the model structure, and neither should be hidden in an unexplained percentage added to the final capital result.

Designing and Recording an Elicitation

A useful elicitation begins with a precise question and a common information set. Experts should understand the same event definition, exposure basis, loss measure, and period. Provide relevant data and explain known limitations, but avoid presenting an anchor that could unduly influence independent estimates. Ask for the reasoning and evidence behind an estimate, not only a number.

For a quantitative estimate, a practical record can include the expert’s central estimate, the unit and period, key evidence, assumptions, and factors that could make the estimate too high or too low. If estimates differ, investigate the reasons before combining them. Differences may reflect genuinely different views, different interpretations of the question, or different information. Aggregation is not a substitute for resolving ambiguity.

Define the target.
State the modeled event or loss, the population and exposure basis, the measurement horizon, and the parameter being estimated.

Prepare the evidence.
Provide relevant internal and external information, explain its limitations, and identify where judgment is needed because evidence is sparse or not comparable.

Elicit and compare estimates.
Record estimates independently where practical, then discuss the reasons for material differences and check that everyone interpreted the target consistently.

Choose and document a method.
Specify how estimates will be selected or combined, the evidence supporting the result, the limitations, and the person or forum responsible for approval.

Incorporate and review.
Map the judgment to the correct model parameter, verify the calculation and units, and retain enough detail for another reviewer to reproduce the change.

The method for combining estimates should be selected for a reason and applied consistently. A median can reduce the influence of an unusually high or low estimate; a weighted average can reflect a pre-established weighting policy or a documented difference in relevant expertise. Neither method is automatically correct. The record should explain why it fits the question and how disagreements were handled.

Incorporating Judgment Without Hiding It

Suppose a model uses a frequency-severity structure. Let $N$ be the number of events over a fixed period and let $X_j$ be the loss from event $j$. Under the compound Poisson assumptions that $N$ is Poisson with mean $\lambda$, event severities are identically distributed with finite mean $\mu$, and severities are independent of the count, aggregate loss is $S=\sum_{j=1}^{N}X_j$. Then the expected aggregate loss is $\lambda\mu$. This is a useful check on the effect of a judgment about frequency or mean severity; it is not, by itself, a capital measure.

E[S]=E\bigl[E[S\mid N]\bigr] =E[N\mu] =\lambda\mu

The justification is conditional expectation. Given $N=n$, the aggregate is a sum of $n$ independent severities, so its conditional expectation is $n\mu$. Taking the expectation over the Poisson count gives $E[N]\mu=\lambda\mu$. If severity depends on event count, the count is not Poisson, or the model uses a different loss structure, this calculation may not apply as written.

A structured judgment should be incorporated at the point in the model that matches its meaning. For example, a judgment about events per exposure-year belongs in the frequency assumption, while an assessment of mean loss conditional on an event belongs in the severity assumption. Applying an adjustment in the parameter and again as a final capital overlay can double count its effect.

Worked Example: Eliciting an Event Rate

A hypothetical insurer has limited history for a newly introduced service line. The model needs an annual event rate per service contract-year for a specifically defined incident. Three operational experts, given the same event definition and exposure basis, provide central estimates of 0.004, 0.005, and 0.012. The approved elicitation protocol uses the median when there are three estimates. The portfolio has 2,400 contract-years, and the assumed mean loss per event is $30,000. Estimate the selected rate and the corresponding expected annual aggregate loss under a Poisson frequency-severity model.

Method. Apply the pre-specified median rule to the three comparable estimates. The ordered estimates are $0.004, 0.005, 0.012$, so the selected rate is $0.005$ events per contract-year. The high estimate is not deleted; its rationale should be investigated and recorded even though the protocol selects the median.

Expected event count. Multiply the selected rate by the number of contract-years:

2{,}400(0.005)=12 \text{ expected events}

Expected aggregate loss. With a Poisson count of mean 12 and independent event losses with mean $30,000, the compound Poisson expectation is:

E[S]=12(\$30{,}000)=\$360{,}000

The result is $360,000 of expected annual aggregate loss. As a check, the portfolio rate is $12/2{,}400=0.005$ per contract-year, which matches the selected rate. The method avoids treating the largest estimate as automatically correct or averaging estimates whose rationale has not been examined.

Using Data and Judgment Together

When data provide a useful but incomplete estimate, judgment may be combined with that estimate under an explicit rule. A weighted average is one possible governance choice, not a universal statistical law. Its weights should be set or approved for a reason, and the calculation should make clear which estimate receives which weight. The result should still be checked against the risk definition and any available evidence.

Worked Example: A Governed Blend of Data and Judgment

A hypothetical portfolio has 1,000 exposure-years of relevant observations and eight recorded events, giving a data-based rate of 0.008 per exposure-year. After reviewing the same event definition, a panel provides a structured central rate estimate of 0.014. The model governance policy for this case specifies a 75% weight on the data estimate and a 25% weight on the panel estimate. For a portfolio of 4,000 exposure-years, assume mean severity of $18,000. Calculate the blended rate and expected aggregate loss.

Method. First calculate the data estimate: $8/1{,}000=0.008$ events per exposure-year. Then apply the stated weights:

$$ 0.75(0.008)+0.25(0.014) =0.006+0.0035 =0.0095 $$

The blended rate is 0.0095 events per exposure-year. For 4,000 exposure-years, the expected event count is:

4{,}000(0.0095)=38 \text{ expected events}

The expected aggregate loss under the stated frequency-severity assumptions is:

38(\$18{,}000)=\$684{,}000

The result is $684,000. The check $38/4{,}000=0.0095$ confirms the portfolio event count is consistent with the blended rate. A common wrong calculation is the unweighted average, $(0.008+0.014)/2=0.011$, which would imply 44 expected events and $792,000 of expected loss. That calculation ignores the approved 75%/25% weighting rule. The weights must be justified and documented; their existence does not make the blend inherently more reliable than either input.

Documenting and Challenging Severity Judgments

A severity judgment should state what the amount measures: for example, gross loss or net loss, loss at a specified price level, or mean severity conditional on an event. Experts should identify the evidence they used, such as changes in repair costs, claims handling, coverage terms, or operating conditions. The model owner should check that the judgment applies to the modeled period and that it is not already reflected in the data, trend assumptions, or another adjustment.

Worked Example: Applying a Severity Adjustment Once

A hypothetical event model uses a historical mean severity of $80,000. After reviewing documented changes in repair specifications and supplier prices, a panel estimates that current mean severity should be 10%, 20%, or 30% above the historical amount; the approved procedure selects the median percentage. The frequency assumption is 0.03 events per exposure-year, and the modeled portfolio contains 1,500 exposure-years. Calculate the selected mean severity and expected aggregate loss.

Method. Order the elicited adjustments: 10%, 20%, 30%. Their median is a 20% increase. Apply it once to the historical mean:

\$80{,}000(1+0.20)=\$96{,}000

The expected event count is:

$$ 1{,}500(0.03)=45 $$

Using the stated frequency and adjusted mean severity, expected aggregate loss is:

45(\$96{,}000)=\$4{,}320{,}000

The answer is $4,320,000. The calculation is consistent with the assumptions: the adjusted severity is 1.2 times the historical mean, and 45 expected events at $96,000 each produce $4.32 million. The method avoids adding the 20% twice—for example, once to severity and again as an unexplained increase to the final loss estimate. If the evidence supports a separate frequency change, that should be assessed and recorded separately.

Challenge, Governance, and Common Traps

A sound challenge asks whether the judgment answers the specified question and whether the underlying rationale is credible and reproducible. It is not a requirement that every expert agree, nor does disagreement alone invalidate an estimate. Reviewers should be able to trace the path from evidence to judgment to model input, and from the input to its effect on model output.

Challenge the definition. Check event, exposure, loss basis, and horizon. A rate for a broader event definition should not be inserted into a narrower model component without adjustment.
Challenge the evidence. Ask whether the information is relevant to the modeled portfolio and period, whether it duplicates information already used, and what important evidence is missing.
Challenge the method. Confirm that the aggregation or weighting rule was specified and applied consistently, and that material differences among experts were investigated.
Challenge implementation. Recalculate the parameter change and trace it to the intended model input. Check units and confirm it has not also been applied elsewhere.
Challenge the record. Require the estimate, rationale, limitations, sensitivity or impact considered, approval, and date to be retained with the model documentation.

A management overlay may be appropriate only when it is clearly identified, supported by a reason that is not already captured, quantified with a reproducible method, and subject to approval and monitoring. “Management believes the answer is too low” is not a sufficient basis for a hidden percentage adjustment. The record should say what evidence prompted the adjustment, which assumption it changes, and how double counting was ruled out.

Key takeaway: Judgment becomes a defensible model input when its target, evidence, elicitation method, calculation, limitations, and approval are explicit. Keep it at the parameter or model component it actually informs; do not conceal it in an unexplained final overlay.

Check Your Understanding

Work each problem using the stated assumptions and distinguish the calculated result from any judgment about whether the assumptions are appropriate.

A structured panel gives annual event-rate estimates of 0.003, 0.006, and 0.008 per device-year. The approved method is the median. A portfolio has 2,500 device-years and mean severity of $12,000. Under a Poisson frequency-severity model, calculate the selected rate and expected aggregate loss. (Answer: rate 0.006 per device-year; expected loss $180,000.)
A data estimate is 0.010 events per exposure-year and a structured expert estimate is 0.022. An approved rule assigns 60% weight to data and 40% to judgment. For 3,000 exposure-years and mean severity of $25,000, calculate the blended rate and expected aggregate loss. (Answer: rate 0.0148; expected loss $1,110,000.)
A historical mean severity is $50,000. Three experts estimate adjustments of 8%, 12%, and 25%; the approved method selects the median adjustment. If there are 20 expected events, calculate adjusted severity and expected aggregate loss. (Answer: adjusted severity $56,000; expected aggregate loss $1,120,000.)
A portfolio’s data-based event rate is 0.005 per policy-year. A panel estimates 0.009, and policy assigns weights of 80% and 20% to data and judgment, respectively. There are 5,000 policy-years and mean severity is $40,000. Calculate the expected event count and aggregate loss. (Answer: blended rate 0.0058; 29 expected events; expected loss $1,160,000.)
A model uses a historical severity mean of $100,000. A documented panel assessment supports a 15% severity increase, and the frequency model already incorporates a separately approved 10% increase in event rate. If the baseline expected event count before that frequency increase is 50 and mean severity is $100,000, calculate expected aggregate loss after both changes. What is the main control against double counting? (Answer: adjusted event count 55; adjusted severity $115,000; expected loss $6,325,000; record the two adjustments at their distinct model inputs and verify neither is applied again as a final overlay.)

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