From blank sheet to working model.

The Domain

Commercial property insurance. A regional carrier with a $340M coastal book is considering a 12% rate increase on properties within 500m of the shoreline. The actuarial team has identified coastal location as a significant predictor of loss. The underwriting team believes the relationship is more complex — that construction quality, not location per se, is the driving variable, and that coastal location is a proxy for the older construction stock that predominates near the shore.

The board question: will the rate increase reduce loss ratio, or will it primarily drive away the better risks while retaining the worse ones?

This is a Rung 2 question. The historical data shows that coastal properties have higher losses. It cannot show what happens when you intervene on price for coastal properties — because the data contains no such intervention. The causal model is required.

Phase 1 — The Decision

The scope of the first model is defined by the board’s question, not by the completeness of available data. The question is: what happens to loss ratio if we increase coastal rates by 12%?

Working backward from this question, the model needs to capture: (1) the causal relationship between price and retention by risk quality — who leaves and who stays when prices rise; (2) the causal relationship between risk quality and loss outcome; (3) the causal relationship between coastal location and both risk quality and loss outcome independently.

This scoping eliminates from the first model all variables that do not connect to these three relationships. Claims severity distribution, reinsurance structure, expense ratio — these matter for the business but do not affect the answer to the board’s specific question. The model is built for a decision, not for comprehensiveness.

Phase 2 — The Graph

The knowledge elicitation session involves the chief underwriter, two senior property underwriters, and the head of claims. The session has two parts: structure first, numbers never.

Structure: the facilitator asks each expert to describe the mechanism connecting each candidate variable to the outcome. “How does coastal location affect loss probability? Through what process? What variable does it operate through?” The answer — consistently from all four experts — is that coastal location predicts construction vintage, which predicts construction quality, which drives loss probability. Location has no direct effect on loss once construction quality is controlled for.

This produces a graph with a mediation structure: Location → Construction Vintage → Construction Quality → Loss Probability. Not Location → Loss Probability directly. The actuarial model, which regressed loss on location, was adjusting for a mediator it did not know was a mediator.

Price sensitivity: the experts agree that price elasticity differs by construction quality. High-quality risks are more price-sensitive (they have more alternatives) and lower-quality risks are less price-sensitive. The graph encodes this as a moderation: Price → Retention, moderated by Construction Quality.

Phase 3 — The Tables

The conditional probability tables are populated from two sources: historical claims data for the outcome nodes, and expert elicitation for the intermediate variables where data is sparse.

The key table is P(Retention | Price Increase, Construction Quality). The experts estimate: high-quality risks, 12% increase → 35% non-renewal. Low-quality risks, 12% increase → 8% non-renewal. This asymmetry is the critical parameter — it encodes the adverse selection mechanism the board needs to understand.

Expert disagreement on this table is substantial: estimates for high-quality non-renewal range from 25% to 45%. The model encodes the disagreement as a wide prior. See When Experts Disagree for the formal treatment. The wide prior propagates into the loss ratio forecast as uncertainty — making the uncertainty visible in the output rather than hiding it in a point estimate.

Phase 4 — The Queries

Forward query (Rung 2): P(Loss Ratio | do(Price = +12%)). The model computes the joint distribution over retention, portfolio mix, and loss outcome after the price intervention. Result: expected loss ratio improvement of 2.1 percentage points, but with a 34% probability of worsening loss ratio due to adverse selection — the wide prior on high-quality non-renewal produces substantial tail risk on the downside.

Counterfactual (Rung 3): What would the loss ratio be if we applied the 12% increase only to properties where Construction Quality is below a threshold? The model evaluates the surgical intervention: selective rate increase on low-quality risks only. Result: 3.4pp loss ratio improvement, adverse selection probability under 8%. The selective intervention dominates the blanket increase on the board’s stated objective.

VOI query: How much would the decision change if we resolved the uncertainty in the high-quality non-renewal parameter? VOI = £2.3M in expected loss ratio improvement — substantially higher than the cost of a targeted broker survey to elicit more precise estimates. The model recommends the survey before committing to the rating action.

What It Produces

Four deliverables: the causal graph (a diagram the underwriting team can debate on a whiteboard and hand to a regulator); the parameterized model (a queryable .bayes file); the three query results with uncertainty bounds; and a recommendation to gather more evidence on the high-quality elasticity parameter before committing to the rating action.

The recommendation is based on the VOI calculation — it is not a judgment call. The model computed that the evidence is worth gathering. That is the discipline the causal model imposes: investigation is recommended when and only when the VOI exceeds the cost. Not when someone feels uncertain. Not when it feels prudent. When the number says so.

The full four-phase engagement process is described on The Four Phases.