insurance-fairness 1.1.0

Proxy discrimination auditing, discrimination-free pricing, and diagnostics for UK insurance pricing models. Implements FCA Consumer Duty and Equality Act 2010 compliance checks.

insurance-fairness

FCA Consumer Duty and Equality Act 2010 compliance auditing for UK insurance pricing models — proxy discrimination detection, exposure-weighted bias metrics, and FCA-ready Markdown audit reports.

Your postcode rating factor probably correlates with ethnicity. The FCA's Consumer Duty (PS22/9) requires you to demonstrate this is not producing indirect discrimination under Section 19 of the Equality Act 2010 — and the FCA's multi-firm review of Consumer Duty implementation (2024) found most insurers' Fair Value Assessments could not do this. insurance-fairness produces the documented, exposure-weighted audit trail your pricing committee can sign off.

Blog post: Your Pricing Model Might Be Discriminating

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Every UK pricing team faces the same problem: postcode encodes protected-characteristic information without anyone ever modelling a protected attribute directly. Citizens Advice (2022) estimated a £280/year ethnicity penalty in UK motor insurance, totalling £213m per year, driven entirely through proxy factors. Proving — or disproving — this is happening in your book is what proxy detection is for.

The compliance risk is live. The FCA's multi-firm review of Consumer Duty implementation (2024) found most Fair Value Assessments were "high-level summaries with little substance". Six Consumer Duty investigations are now open, two of which directly involve insurers on fair value grounds.

This is a compliance audit tool, not a methodology library. It produces documented, evidenced, FCA-mapped analysis that a pricing committee can sign off and that will stand up to an FCA file review. Fairlearn and AIF360 help you satisfy a chosen fairness criterion — they do not answer the question: "Can I demonstrate to the FCA that this model does not constitute indirect discrimination under Section 19 of the Equality Act?"

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Part of the Burning Cost stack

Takes a fitted pricing model and a dataset with protected characteristics. Feeds audit reports and proxy detection results into insurance-governance for pricing committee sign-off packs and FCA Consumer Duty documentation. → See the full stack

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insurance-fairness vs doing it manually

Task	Manual approach	insurance-fairness
Proxy detection	Spearman correlation — misses non-linear relationships; postcode-ethnicity returns |r| ≈ 0.10, finds nothing	CatBoost proxy R² + mutual information; returns R² ≈ 0.62, unambiguously RED — 100% detection rate across 50 seeds
Exposure-weighted A/E by group	Custom code per model, often not exposure-weighted	calibration_by_group() — exposure-weighted, RAG status, 10-decile grid, Equality Act framing
Log-space demographic parity	Multiply predictions, take ratios — silently wrong for multiplicative models	demographic_parity_ratio() — log-ratio for GLM/GBM multiplicative worlds
Financial impact of discrimination	Not quantified	ProxyVulnerabilityScore — per-policyholder £ cost of proxy exploitation
Action vs outcome fairness (Consumer Duty Outcome 4)	Not possible with standard metrics	DoubleFairnessAudit — full Pareto front, Tchebycheff scalarisation, FCA evidence pack
Audit report for pricing committee	Manual Word document, no regulatory mapping	report.to_markdown() — FCA-mapped Markdown with PRIN 2A, FG22/5 cross-references and sign-off table

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Quick start

import polars as pl
from insurance_fairness import FairnessAudit

# df: policy-level DataFrame with claims, exposure, rating factors,
# and a protected characteristic column (or ONS-derived area proxy)
audit = FairnessAudit(
    model=catboost_model,
    data=df,
    protected_cols=["gender"],
    prediction_col="predicted_rate",
    outcome_col="claim_amount",
    exposure_col="exposure",
    factor_cols=["postcode_district", "vehicle_age", "ncd_years", "vehicle_group"],
    model_name="Motor Model Q4 2024",
    run_proxy_detection=True,
)
report = audit.run()
report.summary()
# Overall RAG: RED
# Proxy detection: postcode_district — proxy R²=0.62 [RED], MI=0.41 [RED]
# Calibration by group (gender): max A/E disparity 0.081 [AMBER]
# Demographic parity log-ratio: +0.082 (ratio 1.085) [AMBER]
report.to_markdown("audit_q4_2024.md")  # FCA-ready Markdown with sign-off table

See examples/quickstart.py for a fully self-contained example including synthetic data generation and model fitting.

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Installation

pip install insurance-fairness
# or
uv add insurance-fairness

For the Pareto optimisation subpackage (requires pymoo):

pip install "insurance-fairness[pareto]"

Dependencies: polars, catboost, scikit-learn, scipy, numpy, jinja2, pyarrow

Questions or feedback? Start a Discussion. Found it useful? A star helps others find it.

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Features

• Proxy detection — identifies which rating factors (postcode, vehicle group, occupation) are acting as protected-characteristic proxies using mutual information, CatBoost proxy R², partial correlation, and SHAP-linked price impact
• Exposure-weighted bias metrics — calibration by group (A/E ratio), demographic parity ratio (log-space), disparate impact ratio, equalised odds, Gini by group, Theil index; all weight by earned car-years, not policy count
• Counterfactual fairness — flip protected characteristics and measure premium impact; supports direct flip and LRTW marginalisation
• Proxy vulnerability scoring (ProxyVulnerabilityScore) — per-policyholder £ difference between unaware premium and discrimination-free benchmark; TVaR overcharge, parity cost, fairness range
• Indirect discrimination audit (IndirectDiscriminationAudit) — five benchmark premiums from Côté et al. (2025): aware, unaware, unawareness, proxy-free, parity-cost; no causal graph required
• Multicalibration (MulticalibrationAudit, IterativeMulticalibrationCorrector) — audit and iteratively correct pricing models for multicalibration fairness (Denuit, Michaelides & Trufin, 2026)
• Marginal fairness correction (MarginalFairnessPremium) — closed-form Stage 2 adjustment of Expected Shortfall, Wang transform, or any distortion risk measure to be marginally fair; no iterative solver (Huang & Pesenti, 2025)
• Double fairness (DoubleFairnessAudit) — joint action (Delta_1) and outcome (Delta_2) Pareto optimisation via lexicographic Tchebycheff scalarisation; addresses Consumer Duty Outcome 4 directly (Bian et al., 2026)
• Discrimination-insensitive reweighting (DiscriminationInsensitiveReweighter) — training-data weights that achieve X ⊥ A without removing the protected attribute; KL divergence minimisation (Miao & Pesenti, 2026)
• Privatised audit (PrivatizedFairnessAudit) — fairness auditing when protected attributes are privatised via local differential privacy or estimated from proxies (Zhang, Liu & Shi, 2025)
• Optimal transport (optimal_transport subpackage) — discrimination-free pricing via Lindholm marginalisation, causal path decomposition, Wasserstein barycenter correction
• FCA-mapped audit reports — Markdown with PRIN 2A, FG22/5, Equality Act s.19 cross-references and a sign-off table; suitable for pricing committee packs and FCA file reviews

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Expected performance

On a 20,000-policy synthetic UK motor portfolio with a known postcode-ethnicity proxy structure, replicating the Citizens Advice (2022) finding:

Metric	Manual Spearman (|r| > 0.25)	Library (proxy R² + MI)
postcode_area flagged as proxy	No (|r| ≈ 0.10)	Yes (proxy R² ≈ 0.62, RED)
Factors correctly flagged	0/6	1–2/6
Detection rate across 50 seeds	0%	100%
Non-linear proxy detection	No	Yes (CatBoost)
Financial impact quantified	No	Yes

High-diversity policyholders pay roughly £70–90 more per year than low-diversity policyholders, driven through the postcode area loading. The manual Spearman check returns |r| ≈ 0.10 and finds nothing. The library returns proxy R² ≈ 0.62 — unambiguously RED — because postcode encodes diversity non-linearly across London vs outer vs rural areas.

Task	Time (n=50,000 policies)	Notes
Calibration by group (10 deciles)	< 2s	Primary Equality Act metric
Demographic parity ratio	< 1s	Log-space, multiplicative model
Proxy R-squared (per factor, CatBoost)	15–60s	Per factor; subsample for large books
Mutual information scores	< 5s	Catches non-linear relationships
Full FairnessAudit.run() with proxy detection	2–10 min	Produces FCA-ready Markdown report

Run on Databricks

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Modules

FairnessAudit and FairnessReport

The main entry point. FairnessAudit.run() returns a FairnessReport with:

• report.summary() — plain-text console output
• report.to_markdown(path) — Markdown report with regulatory mapping and sign-off section
• report.to_dict() — JSON-serialisable dict for downstream processing
• report.flagged_factors — list of factors with proxy concerns
• report.overall_rag — 'green', 'amber', or 'red'
• report.results["gender"] — per-characteristic ProtectedCharacteristicReport

bias_metrics

All metrics are exposure-weighted and work on Polars DataFrames.

from insurance_fairness import (
    calibration_by_group,
    demographic_parity_ratio,
    disparate_impact_ratio,
    equalised_odds,
    gini_by_group,
    theil_index,
)

# Calibration by group (sufficiency) — most defensible under Equality Act s.19
cal = calibration_by_group(
    df,
    protected_col="ethnicity_group",
    prediction_col="model_freq",
    outcome_col="n_claims",
    exposure_col="exposure",
    n_deciles=10,
)
print(f"Max A/E disparity: {cal.max_disparity:.4f} [{cal.rag}]")

# Demographic parity ratio (log-space, multiplicative model)
dp = demographic_parity_ratio(df, "gender", "predicted_premium", "exposure")
print(f"Log-ratio: {dp.log_ratio:+.4f} (ratio: {dp.ratio:.4f})")

# Theil index decomposition
theil = theil_index(df, "ethnicity_group", "predicted_premium", "exposure")
print(f"Between-group share: {theil.theil_between / theil.theil_total:.1%}")

proxy_detection

from insurance_fairness import detect_proxies

result = detect_proxies(
    df,
    protected_col="ethnicity_proxy",
    factor_cols=["postcode_district", "vehicle_age", "ncd_years", "driver_age_band"],
    run_proxy_r2=True,
    run_mutual_info=True,
    run_partial_corr=True,
)
print(result.flagged_factors)  # ['postcode_district']
print(result.to_polars())      # Polars DataFrame, sorted by proxy R-squared

counterfactual

from insurance_fairness import counterfactual_fairness

cf = counterfactual_fairness(
    model=model,
    df=df,
    protected_col="gender",
    feature_cols=["gender", "postcode_district", "vehicle_age", "ncd_years"],
    exposure_col="exposure",
    flip_values={"M": "F", "F": "M"},
    method="direct_flip",
)
cf.summary()
# "Counterfactual premium impact: +8.2%"

For models that do not use the protected characteristic directly, use method="lrtw_marginalisation".

double_fairness

v0.6.0. Action fairness (Delta_1) and outcome fairness (Delta_2) are not the same obligation and they can conflict. Minimising premium disparity does not minimise loss ratio disparity. On a 20,000-policy synthetic UK motor portfolio, the policy with the most equal premiums produced the most unequal loss ratios — a compliance gap the FCA's multi-firm review of Consumer Duty implementation (2024) identified.

DoubleFairnessAudit recovers the full Pareto front via lexicographic Tchebycheff scalarisation and selects the value-maximising Pareto point as the recommended operating policy:

from insurance_fairness import DoubleFairnessAudit

audit = DoubleFairnessAudit(n_alphas=20)
audit.fit(
    X_train,       # features excluding protected attribute
    y_premium,     # primary outcome: pure premium
    y_loss_ratio,  # fairness outcome: claims / premium
    S_gender,      # binary protected group indicator
)
result = audit.audit()
print(result.summary())
fig = audit.plot_pareto()
print(audit.report())   # FCA Consumer Duty Outcome 4 evidence section

Run the benchmark on Databricks

marginal_fairness

v0.5.0. Closed-form Stage 2 correction for distortion risk measure premiums — Expected Shortfall, Wang transform, or any custom distortion — to be marginally fair with respect to protected attributes. No iterative solver (Huang & Pesenti, 2025).

from insurance_fairness import MarginalFairnessPremium

mfp = MarginalFairnessPremium(distortion='es_alpha', alpha=0.75)
mfp.fit(Y_train, D_train, X_train, model=glm, protected_indices=[0])
rho_fair = mfp.transform(Y_test, D_test, X_test)

report = mfp.sensitivity_report()
print(f"Baseline ES0.75: {report.rho_baseline:.4f}")
print(f"Fair ES0.75:     {report.rho_fair:.4f}")

indirect

v0.6.4. End-to-end partition-based audit of indirect discrimination. Computes five benchmark premiums from Côté et al. (2025): aware, unaware, unawareness, proxy-free, and parity-cost. Proxy vulnerability = mean |h_U(x) - h_A(x)| quantifies how much the unaware model exploits proxies. No causal graph required.

from insurance_fairness import IndirectDiscriminationAudit

audit = IndirectDiscriminationAudit(
    protected_attr="gender",
    proxy_features=["postcode_district", "occupation"],
    exposure_col="exposure",
)
result = audit.fit(X_train, y_train, X_test, y_test)
print(f"Proxy vulnerability: {result.proxy_vulnerability:.2f}")
print(result.segment_report)

multicalibration

v0.3.7+. Audit and correct pricing models for multicalibration fairness — the model should be well-calibrated not just in aggregate, but within every protected-group × risk-decile cell (Denuit, Michaelides & Trufin, 2026). IterativeMulticalibrationCorrector (v0.6.7) applies iterative recalibration across cells.

from insurance_fairness import MulticalibrationAudit, IterativeMulticalibrationCorrector

audit = MulticalibrationAudit(n_bins=10, alpha=0.05)
report = audit.audit(y_true, y_pred, protected, exposure)
corrected = audit.correct(y_pred, protected, report, exposure)

discrimination_insensitive

v0.6.3. Training-data reweighting that achieves X ⊥ A without removing the protected attribute from the training data. Weights integrate with any sklearn sample_weight parameter (Miao & Pesenti, 2026).

from insurance_fairness import DiscriminationInsensitiveReweighter

rw = DiscriminationInsensitiveReweighter(protected_col="gender")
weights = rw.fit_transform(X_train)
model.fit(X_train.drop("gender", axis=1), y_train, sample_weight=weights)
diag = rw.diagnostics(X_train)

optimal_transport subpackage

Discrimination-free pricing via Lindholm marginalisation, causal path decomposition, and Wasserstein barycenter correction:

from insurance_fairness.optimal_transport import (
    CausalGraph,
    DiscriminationFreePrice,
    FCAReport,
)

diagnostics subpackage

Proxy discrimination diagnostics with D_proxy scalar, Shapley attribution, and per-policyholder vulnerability scores:

from insurance_fairness.diagnostics import ProxyDiscriminationAudit

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Limitations

• The proxy detection thresholds are not FCA-prescribed. Proxy R-squared thresholds (amber: >0.05, red: >0.10) are operationally derived, not regulatory requirements. A factor below the red threshold may still constitute indirect discrimination under Section 19 — the statistical test is a trigger for investigation, not a compliance safe harbour.
• Proxy detection requires a protected characteristic column, which most insurers do not hold. Joining ONS 2021 Census LSOA ethnicity proportions to postcode data is an area-level proxy, not individual-level. Factor correlations with this proxy are correlations with area demographics, not individual ethnicity.
• Calibration by group is not counterfactual fairness. Equal calibration (A/E = 1.0) within each protected group means the model is correctly pricing the proxy-contaminated risk profile — not that it is pricing independent of the protected characteristic.
• The Markdown audit report is evidence, not a compliance determination. It does not constitute legal advice or a regulatory safe harbour. Whether a specific model constitutes indirect discrimination depends on the proportionality justification for the rating factor, which requires expert legal and actuarial judgement outside the scope of this library.

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References

Lindholm, Richman, Tsanakas, Wüthrich (2022). Discrimination-Free Insurance Pricing. ASTIN Bulletin 52(1), 55–89.

Lindholm, Richman, Tsanakas, Wüthrich (2026). Sensitivity-Based Measures of Discrimination in Insurance Pricing. European Journal of Operational Research.

Denuit, Michaelides & Trufin (2026). Multicalibration in Insurance Pricing. arXiv:2603.16317.

Zhang, Liu & Shi (2025). Discrimination-Free Insurance Pricing with Privatized Sensitive Attributes. arXiv:2504.11775.

Côté, O., Côté, M.-P., and Charpentier, A. (2025). A Scalable Toolbox for Exposing Indirect Discrimination in Insurance Rates. CAS Working Paper.

Huang, F. & Pesenti, S. M. (2025). Marginal Fairness: Fair Decision-Making under Risk Measures. arXiv:2505.18895.

Bian, Z., Wang, L., Shi, C., Qi, Z. (2026). Double Fairness Policy Learning: Integrating Action Fairness and Outcome Fairness in Decision-making. arXiv:2601.19186v2.

Miao, K. E. & Pesenti, S. M. (2026). Discrimination-Insensitive Pricing. arXiv:2603.16720.

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Related libraries

Library	What it does
insurance-causal	Double Machine Learning for causal treatment effects — establishes whether a factor genuinely drives risk or proxies a protected characteristic
insurance-governance	Pricing committee sign-off packs and FCA Consumer Duty documentation
insurance-monitoring	Post-bind drift detection — flags when protected-group A/E ratios are shifting in the live book
insurance-optimise	Constrained rate change optimisation with FCA PS21/5 compliance

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