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✅ '''Positivity assumption''' stipulates that within every stratum of observed covariates in a study population, each individual must have a strictly positive probability of receiving each treatment level. In insurance [[Definition:Causal inference | causal inference]], this condition ensures that [[Definition:Underwriting | underwriting]] or pricing interventions being evaluated have actually been applied — and withheld — across all observable risk profiles, so that the causal effect can be identified from the data rather than extrapolated. When an [[Definition:Insurance carrier | insurer]] studies whether a mandatory vehicle inspection requirement reduces [[Definition:Motor insurance | motor]] [[Definition:Claims frequency | claims frequency]], positivity requires that for every age–vehicle–region combination in the data, some policyholders were inspected and some were not.

⚙️ Structural and random violations each pose distinct challenges. Structural violations occur when [[Definition:Insurance policy | policy]] rules or [[Definition:Regulatory compliance | regulations]] deterministically assign treatment — for instance, if all buildings above a certain height are required to carry [[Definition:Terrorism insurance | terrorism coverage]], there is no variation among tall buildings, and the causal effect of terrorism coverage for that subgroup is unidentifiable. Random (or practical) violations arise when certain covariate cells simply contain too few observations in one treatment arm, a frequent occurrence in specialty lines like [[Definition:Cyber insurance | cyber]] or [[Definition:Directors and officers (D&O) liability insurance | D&O]] where portfolios are smaller and risk profiles more heterogeneous. Analysts diagnose these violations by examining the distribution of [[Definition:Propensity score | propensity scores]]; extreme scores near zero or one flag regions of the covariate space where positivity is tenuous. Trimming, truncation, or restricting the target population are standard remedies.

🎯 Overlooking positivity violations can silently undermine analyses that drive material decisions. A [[Definition:Reinsurance | reinsurer]] relying on a causal study to price a [[Definition:Quota share | quota share]] treaty will demand assurance that the underlying analysis was not driven by a handful of observations with near-deterministic treatment assignment and correspondingly extreme weights. In the growing field of [[Definition:Insurtech | insurtech]], where [[Definition:Machine learning | machine learning]] models are increasingly paired with causal estimators to justify algorithmic [[Definition:Rating factor | rating factors]], demonstrating positivity is a prerequisite for regulatory approval in multiple jurisdictions. Practically, the assumption pushes analytical teams toward intellectual honesty about the boundaries of their evidence — acknowledging where the data can speak to causal effects and where it cannot.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Overlap assumption]]
* [[Definition:Propensity score]]
* [[Definition:Causal inference]]
* [[Definition:Common support]]
* [[Definition:Potential outcomes framework]]
* [[Definition:Selection bias]]
{{Div col end}}

Definition:Positivity assumption - Revision history

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