insurance-fairness 0.3.6

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

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Your postcode rating factor is probably an ethnicity proxy. Here's how to prove it — and document it for the FCA.

UK insurers face a genuine compliance obligation to demonstrate their pricing models do not discriminate against customers with protected characteristics. The FCA Consumer Duty (PRIN 2A, live July 2023) requires firms to monitor whether their products provide fair value for different groups of customers, and the FCA's multi-firm review (2024) found most insurers were doing this inadequately. The Equality Act 2010 Section 19 independently prohibits indirect discrimination through rating factors that act as proxies for protected characteristics.

The practical problem is well-documented. Citizens Advice (2022) found a £280/year ethnicity penalty in UK motor insurance in postcodes where more than 50% of residents are people of colour, estimated at £213m per year. The mechanism is straightforward: insurers use postcode as a rating factor; postcode correlates with ethnicity; the postcode effect on price therefore contains an ethnicity component that cannot be justified on pure risk grounds.

Every Python fairness library was built for binary classification or generic regression. None handles the multiplicative frequency/severity structure, exposure-weighted metrics, or the log-link world that pricing actuaries actually work in. This library fills that gap for the UK market.

Why bother

Benchmarked on synthetic UK motor data (50,000 policies) with a known postcode-ethnicity proxy issue, replicating the Citizens Advice (2022) finding structure.

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
SHAP proxy scores	1–5 min	Links proxy correlation to price impact
Full FairnessAudit.run() with proxy detection	2–10 min	Produces FCA-ready Markdown report

The library surfaces proxy concerns that a direct A/E comparison by group will miss. A factor with a postcode proxy R-squared > 0.10 is contributing discriminatory variation to prices — even when A/E by group looks flat.

▶ Run on Databricks

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Blog post: Your Pricing Model Might Be Discriminating — the Lindholm-Richman-Tsanakas-Wüthrich framework explained, the Citizens Advice data in full, and what a defensible audit trail looks like.

What This Library Does

• Identifies which rating factors act as proxies for protected characteristics (mutual information, CatBoost proxy R-squared, partial correlations, SHAP proxy scores)
• Computes exposure-weighted fairness metrics appropriate for insurance: calibration by group, demographic parity ratio in log-space, disparate impact ratio, Gini by group, Theil index
• Runs counterfactual fairness tests by flipping protected characteristics and measuring premium impact
• Produces structured Markdown audit reports with explicit FCA regulatory mapping, suitable for pricing committee packs and FCA file reviews

Installation

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

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

Quick Start

import numpy as np
import polars as pl
from catboost import CatBoostRegressor
from insurance_fairness import FairnessAudit

# Synthetic UK motor portfolio — 1,000 policies
rng = np.random.default_rng(42)
n = 1_000

# Protected characteristic: gender (binary)
gender       = rng.choice(["M", "F"], size=n)
vehicle_age  = rng.integers(1, 15, n).astype(float)
driver_age   = rng.integers(21, 75, n).astype(float)
ncd_years    = rng.integers(0, 9, n).astype(float)
vehicle_group = rng.choice(["A", "B", "C", "D"], size=n)
postcode_district = rng.choice(["SW1", "E1", "M1", "B1", "LS1"], size=n)
exposure     = rng.uniform(0.3, 1.0, n)

# Claim amount: slight gender correlation via vehicle_age proxy
claim_amount = np.exp(
    4.5
    + 0.05 * vehicle_age
    - 0.01 * ncd_years
    + 0.08 * (gender == "M").astype(float)  # injected disparity
    + rng.normal(0, 0.4, n)
) * exposure

# Fit a simple CatBoost frequency model inline
feature_cols = ["vehicle_age", "driver_age", "ncd_years"]
X = np.column_stack([vehicle_age, driver_age, ncd_years])
y = claim_amount / exposure

model = CatBoostRegressor(iterations=100, verbose=0)
model.fit(X, y)

# predicted_rate is the model output on the rate scale (claims per unit exposure).
# Do not multiply by exposure here: calibration_by_group expects a rate and
# multiplies by exposure internally when computing sum(predicted * exposure).
predicted_rate = model.predict(X)

df = pl.DataFrame({
    "gender":            gender,
    "vehicle_age":       vehicle_age,
    "driver_age":        driver_age,
    "ncd_years":         ncd_years,
    "vehicle_group":     vehicle_group,
    "postcode_district": postcode_district,
    "exposure":          exposure,
    "claim_amount":      claim_amount,
    "predicted_rate":    predicted_rate,
})

audit = FairnessAudit(
    model=model,
    data=df,
    protected_cols=["gender"],            # or ethnicity proxy from ONS LSOA data
    prediction_col="predicted_rate",      # rate, not total — calibration_by_group multiplies by exposure
    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()                         # print to console
report.to_markdown("audit_q4_2024.md")  # write FCA-ready report

Note that factor_cols may include factors not used as model inputs. The audit checks for proxy contamination in both model inputs and non-model factors — a factor that is not in the model can still correlate with protected characteristics and inform future model development decisions. In this example, postcode_district and vehicle_group are included in the audit even though neither is a feature in the fitted model.

Output example

The output below is from running the quickstart code above (n=1,000 policies, seed=42). With this small synthetic dataset and no real postcode-ethnicity correlation in the data, proxy detection finds nothing. The RED calibration status reflects noise at small n — try n=50,000 for a more representative audit.

============================================================
Fairness Audit: Motor Model Q4 2024
Date: 2026-03-19
Policies: 1,000 | Exposure: 645.5
Overall status: RED
============================================================

Protected characteristic: gender
----------------------------------------
  Demographic parity log-ratio: -0.0002 (ratio: 0.9998) [GREEN]
  Max calibration disparity: 1.5887 [RED]
  Disparate impact ratio: 0.9922 [GREEN]
  No factors flagged as proxies.

No rating factors flagged with proxy concerns.

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
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 mutual_information_scores, proxy_r2_scores, shap_proxy_scores
from insurance_fairness.proxy_detection import detect_proxies

# Combined proxy detection report
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%"
# (gender=M policyholders would pay 8.2% less if recorded as gender=F)

For models that do not use the protected characteristic directly, use method="lrtw_marginalisation": predictions are averaged over the marginal distribution of the protected characteristic, approximating the Lindholm-Richman-Tsanakas-Wüthrich discrimination-free price.

report

from insurance_fairness.report import generate_markdown_report

md = generate_markdown_report(report)
# Returns a Markdown string with:
# - Executive summary with RAG statuses
# - Per-characteristic metric tables and calibration grids
# - Proxy detection results
# - Regulatory compliance framework mapping
# - Methodology section with academic references
# - Sign-off table for senior actuary attestation

Fairness Criteria and Their Insurance Relevance

The library implements three distinct criteria. They are not equivalent and cannot all be satisfied simultaneously when base rates differ across groups (Chouldechova, 2017).

Calibration by group (sufficiency) — the primary criterion for UK compliance. If the model is equally well-calibrated (A/E = 1.0) for all protected-characteristic groups at each pricing level, any premium differences reflect genuine risk differences. This is defensible under the Equality Act proportionality test and maps directly to the FCA's requirement to demonstrate fair value by group.

Demographic parity — equal average prices across groups. Not required by the Equality Act (which allows risk-based differences), but flagged because large disparities warrant investigation. Reported in log-space, which is the natural metric for multiplicative pricing models.

Counterfactual fairness — premiums do not change when the protected characteristic is flipped. The strictest criterion. Appropriate for characteristics that are direct model inputs and that the regulator prohibits as rating factors (e.g. sex in motor insurance post-Test-Achats).

Proxy Detection Methodology

The library detects proxies using three complementary methods:

Proxy R-squared: A CatBoost model predicts the protected characteristic from each rating factor in isolation. High R-squared means the factor carries substantial information about the protected characteristic. Threshold: R-squared > 0.05 (amber), > 0.10 (red).

Mutual information: Model-free measure of statistical dependence. Captures non-linear relationships that R-squared may miss. Useful as a complement to R-squared for categorical factors.

SHAP proxy scores: For each factor, the Spearman correlation between its SHAP contribution to the price prediction and the protected characteristic. This links proxy correlation to actual price impact — a factor with high proxy R-squared but low SHAP correlation is correlated with the protected characteristic but not contributing to discriminatory prices.

These thresholds are not prescribed by the FCA. Treat them as triggers for investigation rather than bright-line compliance tests.

Data Requirements

The protected characteristic column can be:

• Binary (0/1 or string): common for gender, disability indicator
• Multi-category string: e.g. driver age band as a protected characteristic
• Continuous proxy: ONS Census 2021 LSOA ethnicity proportion joined to postcode

For ethnicity, the recommended approach for UK insurers:

1. Download ONS Postcode Directory (ONSPD) from the ONS Geography Portal
2. Download 2021 Census Table TS021 (Ethnic group by LSOA) from NOMIS
3. Join postcode -> LSOA -> ethnicity proportion
4. Use the "% non-white British" at LSOA level as a continuous ethnicity proxy

The library does not bundle this data (it is large and updated quarterly). The join logic is straightforward and can be done in Polars before passing to FairnessAudit.

Regulatory Context

FCA Consumer Duty (PRIN 2A.4): Firms must monitor and demonstrate fair value across groups of customers defined by protected characteristics. The FairnessReport output and its calibration by group metrics directly satisfy this monitoring requirement.

Equality Act 2010, Section 19 (Indirect Discrimination): A rating factor that puts persons sharing a protected characteristic at a particular disadvantage constitutes indirect discrimination unless justified as a proportionate means of achieving a legitimate aim. The proxy detection module identifies which factors are at risk of constituting indirect discrimination.

FCA Evaluation Paper EP25/2 (2025): EP25/2 evaluates whether the GIPP price-walking remedies achieved their intended outcomes. It is a backward-looking evaluation paper, not a compliance instrument, and imposes no obligations on firms. It is not about proxy discrimination or protected characteristics monitoring.

The FCA has not prescribed a specific methodology. The academic framework underlying this library (Lindholm, Richman, Tsanakas, Wüthrich, 2022-2026) has strong credentials — published in ASTIN Bulletin and the European Journal of Operational Research, and awarded by the American Academy of Actuaries. Using a published, peer-reviewed methodology is more defensible than a bespoke approach.

Academic References

• Lindholm, Richman, Tsanakas, Wüthrich (2022). Discrimination-Free Insurance Pricing. ASTIN Bulletin 52(1), 55-89.
• Lindholm, Richman, Tsanakas, Wüthrich (2023). A Multi-Task Network Approach for Calculating Discrimination-Free Insurance Prices. European Actuarial Journal.
• Lindholm, Richman, Tsanakas, Wüthrich (2024). What is Fair? Proxy Discrimination vs. Demographic Disparities in Insurance Pricing. Scandinavian Actuarial Journal 2024(9).
• Lindholm, Richman, Tsanakas, Wüthrich (2026). Sensitivity-Based Measures of Discrimination in Insurance Pricing. European Journal of Operational Research.
• Citizens Advice (2022). Discriminatory Pricing: Exploring the Ethnicity Penalty in the Insurance Market.
• FCA Consumer Duty Finalised Guidance FG22/5 (2023).
• FCA Multi-Firm Review: Outcomes Monitoring under the Consumer Duty (2024).
• FCA Thematic Review TR24/2: General Insurance and Pure Protection Product Governance (2024).
• FCA Evaluation Paper EP25/2: Our General Insurance Pricing Practices Remedies (2025).

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Capabilities Demo

Demonstrated on synthetic UK motor data (50,000 policies) with a known fairness issue: postcode correlates with an ethnicity proxy, replicating the Citizens Advice (2022) finding. Full notebook: notebooks/fairness_audit_demo.py.

• Proxy detection using mutual information, CatBoost proxy R-squared, SHAP proxy scores, and partial correlations — identifies which rating factors carry indirect protected-characteristic information
• Exposure-weighted fairness metrics: calibration by group, demographic parity ratio in log-space, disparate impact ratio, Gini by group, Theil index — all computed correctly for a multiplicative pricing model
• Counterfactual fairness test: flips postcode/proxy values and measures premium impact on the same underlying risk
• Structured Markdown audit report with explicit FCA Consumer Duty (PRIN 2A) and Equality Act 2010 Section 19 regulatory mapping, suitable for pricing committee packs and FCA file reviews
• Pareto optimisation notebook demonstrates the fairness-accuracy trade-off curve: how much predictive performance is lost at each level of fairness constraint

When to use: Before any model goes to production pricing, and at regular intervals thereafter. The FCA's 2024 multi-firm review found most insurers were auditing inadequately. An audit that cannot answer "does this factor act as an ethnicity proxy?" is not sufficient under Consumer Duty.

Other Burning Cost libraries

Model building

Library	Description
shap-relativities	Extract rating relativities from GBMs using SHAP
insurance-interactions	Automated GLM interaction detection via CANN and NID scores
insurance-cv	Walk-forward cross-validation respecting IBNR structure

Uncertainty quantification

Library	Description
insurance-conformal	Distribution-free prediction intervals for Tweedie models
bayesian-pricing	Hierarchical Bayesian models for thin-data segments
insurance-credibility	Bühlmann-Straub credibility weighting

Deployment and optimisation

Library	Description
insurance-deploy	Champion/challenger framework with ENBP audit logging
insurance-causal	Causal inference — establishes whether a rating factor causally drives risk or is a proxy for a protected characteristic
insurance-optimise	Constrained rate change optimisation with FCA PS21/5 compliance

Governance

Library	Description
insurance-governance	PRA SS1/23 model validation reports
insurance-monitoring	Model monitoring: PSI, A/E ratios, Gini drift test

All libraries and blog posts →

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Benchmark: Proxy discrimination detection

20,000 synthetic UK motor policies with a known postcode–ethnicity proxy structure. London postcode areas are assigned a diversity score of ~0.70, outer cities ~0.40, and rural areas ~0.20. Six rating factors are tested: postcode_area, vehicle_group, ncd_years, age_band, annual_mileage, payment_method. The protected attribute (diversity score) is never given to the model — only present for detection.

The benchmark compares a standard manual check (pairwise Spearman correlation) against the library's three-method approach (proxy R², mutual information, SHAP proxy scores).

Factor	Spearman r (manual)	Proxy R² (library)	MI (nats)	SHAP proxy score	Library status
postcode_area	0.0634	0.7767	0.8169	0.7513	RED
vehicle_group	0.0160	0.0000	0.0019	0.0040	GREEN
ncd_years	−0.0050	0.0000	0.0063	0.0116	GREEN
age_band	−0.0045	0.0000	0.0025	0.0329	GREEN
annual_mileage	−0.0034	0.0000	0.0056	0.0031	GREEN
payment_method	0.0094	0.0000	0.0038	n/a	GREEN

Manual Spearman check: 0/6 factors flagged (all |r| < 0.25).
Library proxy_r2 + MI: 1/6 factors flagged (postcode_area RED).

Timing (n=20,000 policies, measured on Databricks serverless):

Task	Measured time
Proxy R² (6 factors, CatBoost, 80 iterations)	0.5s
Mutual information scores	included
SHAP proxy scores (CatBoost, 150 iterations)	included
Full benchmark end-to-end	4.1s

Key findings

• The Spearman correlation check returns 0/6 flagged — all correlations are below 0.25. It completely misses the postcode proxy. The relationship is non-linear and categorical: postcode area encodes group identity rather than a monotone ordering, so rank correlation cannot detect it.
• The library's CatBoost proxy R² for postcode_area is 0.78 — a single postcode area variable accounts for 78% of the variance in the ethnicity diversity score. That is a near-certain proxy relationship. Mutual information (0.82 nats) confirms it independently.
• The SHAP proxy score of 0.75 for postcode_area shows that the proxy relationship is not dormant — it is actively propagating into model prices. A factor can have high proxy R² but low SHAP proxy score if it is in the model but poorly weighted; here, the full chain from factor to protected attribute to price impact is present.

At n=50,000 the proxy R² scales roughly linearly; expect ~1s per factor. For portfolios above 250,000 policies, the proxy R² fits run on a 50,000-row subsample by default (configurable). The metrics themselves use all rows.

Related Libraries

Library	What it does
insurance-governance	PRA SS1/23 model validation reports — fairness audit outputs feed directly into the governance sign-off pack
insurance-causal	Causal inference — establishes whether a rating factor causally drives risk or is a proxy for a protected characteristic
insurance-synthetic	Synthetic portfolio generation — generate test data with known proxy structure to validate the audit pipeline

Licence

BSD-3

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