Actuarial Pricing Models: GLMs, GBMs & AI Tools for P&C Ratemaking

What Is an Actuarial Pricing Model?

An actuarial pricing model produces the technical price for an insurance risk — the premium required to cover expected losses, loss adjustment expenses, underwriting expenses, and a target profit margin. For P&C lines, pricing models are built on historical claims data and estimate how expected costs vary across policyholder and risk characteristics: geography, coverage type, vehicle class, construction type, industry code, driver or policyholder profile.

The technical price is not the same as the offered premium. The actuarial technical price is the actuarially indicated pure premium — what the math says the risk should cost. The offered premium also incorporates competitive positioning, elasticity of demand, strategic growth or contraction goals, and regulatory constraints. Actuarial pricing platforms like Earnix and hyperexponential hx sit at the boundary: they take the actuarial technical price as input and produce the final offered rate that balances technical adequacy with business goals.

For most P&C lines, actuarial pricing models are structured in three layers:

1. Frequency model: models the expected number of claims per unit of exposure (e.g., claims per earned car-year). A Poisson GLM with a log link is standard for most lines.
2. Severity model: models the expected cost per claim conditional on a claim occurring. A gamma GLM with a log link is standard; for heavy-tailed lines (GL, umbrella, WC medical), log-normal or Tweedie distributions may be more appropriate.
3. Pure premium: frequency × severity = expected cost per unit of exposure. The pure premium is the actuarial foundation for the filed rate. Add expense loading and profit margin to reach the gross written premium per unit.

GLM Ratemaking: The Industry Standard

Generalized linear models have been the P&C actuarial pricing standard since the CAS published foundational papers in the early 2000s. The GLM's dominance in P&C ratemaking is not technical conservatism — it reflects genuine advantages: multiplicative rate structure that matches how ISO rates are actually structured, regulatory interpretability (factor relativities can be explained to state insurance regulators), and ASOP No. 12 compliance (Actuarial Standard of Practice on Credibility Procedures).

The standard personal auto P&C GLM has this form:

E[Frequency] = exp(β₀ + β₁·Territory + β₂·VehicleAge + β₃·DriverAge + β₄·Coverage)
E[Severity | Claim] = exp(γ₀ + γ₁·Territory + γ₂·ClaimType + γ₃·BodyInjuryLimits)
Pure Premium = E[Frequency] × E[Severity | Claim]

Each exponentiated coefficient is a multiplicative relativity: exp(β₁) for territory X means risks in that territory are expected to have exp(β₁) times the frequency of the base territory, holding all other factors constant. Relativities above 1.0 are surcharges; below 1.0 are credits. The actuary reviews these relativities for actuarial reasonableness — do they move in expected directions, are they credible given the data volume, are there interactions the single-variable model misses?

GLM implementation in R:

# Frequency model — Poisson with log link
freq_model <- glm(
  claim_count ~ territory + vehicle_age + driver_age_band + coverage_type,
  family = poisson(link = "log"),
  data = policy_data,
  offset = log(earned_car_years)
)

# Severity model — Gamma with log link
sev_model <- glm(
  paid_loss ~ territory + claim_type + bi_limit_band,
  family = Gamma(link = "log"),
  data = claims_data[claims_data$claim_count > 0, ]
)

# Extract relativities
freq_rel <- exp(coef(freq_model))
sev_rel  <- exp(coef(sev_model))

GLM in Python (statsmodels):

import statsmodels.api as sm
import numpy as np

# Frequency model
freq_model = sm.GLM(
    endog=df['claim_count'],
    exog=sm.add_constant(pd.get_dummies(df[['territory','vehicle_age','driver_age_band']], drop_first=True)),
    family=sm.families.Poisson(link=sm.families.links.Log()),
    offset=np.log(df['earned_car_years'])
).fit()

# Extract relativities
relativities = np.exp(freq_model.params)

Credibility Theory in Actuarial Pricing

Credibility is how actuaries blend company experience with industry data when the company's own data is insufficient to produce a fully credible indication. ASOP No. 25 (Credibility Procedures) governs when and how credibility weighting is applied. Two approaches dominate:

Limited fluctuations credibility (CAS standard): determines whether a data subset has enough observations to be treated as fully credible for a given statistic. The CAS standard for frequency is the n that produces a 90% probability that the observed frequency is within ±5% of the true frequency — approximately 1,082 expected claims at the 90/5 standard. A subdivision with fewer than 1,082 expected claims requires blending with external data:

Z = min(sqrt(n / 1082), 1.0)   # credibility weight
Indicated rate = Z × company indication + (1 - Z) × external indication

Bühlmann credibility (Greatest Accuracy, or empirical Bayes): estimates the credibility weight from the data itself by partitioning variance into within-group (process) variance and between-group (parameter) variance. This is more sophisticated than the limited fluctuations approach and is particularly useful in commercial lines or specialty lines where the CAS frequency standard produces very low credibility weights. Bühlmann's k parameter:

k = E[s²(x)] / Var(μ(x))   # ratio of within-group to between-group variance
Z_Bühlmann = n / (n + k)

For pricing actuaries working in R, the actuar package implements both limited fluctuations and Bühlmann credibility. Claude can help actuaries select between approaches, calculate credibility weights for specific data situations, and draft the ASOP No. 25 credibility disclosure paragraph for rate filings.

Machine Learning in Actuarial Pricing

GBMs (gradient boosting machines, including XGBoost and LightGBM) have entered the actuarial pricing toolkit but occupy a specific role — they complement GLMs rather than replacing them. The regulatory and interpretability constraints on P&C rate filings mean pure ML pricing models are rarely filed directly with state regulators. State insurance departments expect actuaries to justify each rating factor and its relativity; an XGBoost model with 300 trees and interaction effects is not a filing-ready deliverable.

The productive pattern is sequential: fit the GLM first for regulatory compliance and interpretability, then fit a GBM on GLM residuals to identify systematic pricing inadequacy that the GLM's additive structure missed.

import xgboost as xgb
import pandas as pd

# Step 1: GLM pure premium prediction
df['glm_pred_pp'] = freq_model.predict() * sev_model.predict()

# Step 2: GLM residual (actual vs. predicted ratio)
df['glm_residual'] = df['actual_pure_premium'] / df['glm_pred_pp']

# Step 3: GBM on residuals to find missed interactions
residual_model = xgb.XGBRegressor(
    n_estimators=300, max_depth=4, learning_rate=0.05,
    subsample=0.8, colsample_bytree=0.8
)
residual_model.fit(
    df[['territory','vehicle_age','driver_age_band','credit_score','telematics_score']],
    df['glm_residual']
)

# Step 4: Feature importance identifies which interactions GLM missed
importance = residual_model.feature_importances_

If the GBM finds that the interaction of credit_score × territory explains significant residual variance, the actuary can add that interaction term to the GLM explicitly — maintaining regulatory interpretability while capturing the predictive improvement. This two-stage approach is the CAS and IFoA recommended workflow for ML in ratemaking.

Telematics and Alternative Data in Actuarial Pricing

Usage-based insurance (UBI) and telematics pricing models have introduced new rating variables that traditional GLMs were not designed to handle: driving behavior scores (braking events per mile, hard acceleration, night driving proportion), odometer readings, and real-time trip data. These are continuous variables with non-linear effects — a driver who brakes hard occasionally is not linearly more risky than one who never does; the effect saturates and interacts with speed context.

For telematics rating, the industry has converged on a hybrid approach: a telematics score (a composite index that translates raw behavior metrics into a single number from 0–100) is added as a rating variable to the standard GLM. The score's GLM relativity is then interpretable and fileable. The scoring model that produces the composite from raw telematics data is proprietary and actuarially reviewed separately.

Claude is useful in telematics pricing for drafting the score model documentation, writing the regulatory narrative explaining how the composite score was constructed and why it is actuarially justified, and helping actuaries prepare the response to state insurance department data requests during the rate filing review.

Rate Change Indication Process

Beyond building the pricing model, P&C actuaries run the annual rate change process: calculating how much the current filed rates deviate from the actuarial indicated rates, given trend, development, and expense changes. The standard indication formula:

Indicated Rate Change = [(Trended, Developed Loss + LAE Ratio + Expense Ratio) / Target Loss Ratio] - 1

Where:
  Trended, Developed Loss Ratio = On-level Incurred Loss Ratio × Trend Factor × Development Factor
  Trend Factor = (1 + freq_trend) × (1 + sev_trend) applied over the trend period
  Development Factor = ultimate / current incurred (from development triangle)
  Target Loss Ratio = 1 - Expense Ratio - Target Profit Margin

This is the actuarial heart of the rate filing. The actuary selects trend factors, development factors, and the expense load, then documents each selection for the state regulator. Claude helps actuaries draft the rate filing narrative — the explanation of why each assumption was selected, how trend credibility was assessed, and why the indicated change is reasonable given the economic environment.

Actuarial Pricing Platforms

The dedicated actuarial pricing platforms occupy a different tier from open-source GLM tools — they handle the business optimization layer, not just the technical pricing layer.

Earnix is the market leader in P&C pricing optimization — translating the actuarial technical price into a competitive offered rate that maximizes portfolio value. Earnix uses ML-based elasticity modeling to understand how proposed prices affect conversion and retention, then recommends offered rates that hit growth and profitability targets simultaneously. It is not an actuarial modeling tool in the ratemaking sense — it is the commercial pricing optimization layer downstream of the actuarial indication. Integration with GLM outputs is standard.

Hyperexponential hx is a modern SaaS pricing platform designed for specialty and commercial lines where each risk requires individual underwriter judgment alongside the model. Hx provides an actuarial model workbench with versioning, collaboration, and deployment capabilities — actuaries build pricing models in hx, underwriters use them to quote. It is particularly strong for lines where pricing models are smaller (less data) and need more frequent iteration.

WTW Radar / RiskAgility is the WTW actuarial pricing modeling platform, widely used in UK and European personal lines. Radar handles both GLM and ML ratemaking workflows in an IDE-style environment designed for actuaries. The WTW Insurance Consulting and Technology division uses it for ratemaking engagement delivery.

SAS Viya / SAS Predictive Modeling remains widely used at large P&C carriers, particularly those with existing SAS analytics infrastructure. SAS offers a full actuarial modeling workflow from data preparation through GLM and GBM modeling to deployment, with model governance and regulatory documentation support. The SAS Path to Production capability for pricing models has enterprise governance features comparable to Milliman Mind NoCode for reserving.

Open-source (R and Python) is the entry point for most actuarial pricing work. The CAS publishes a freely available monograph on GLM ratemaking (Anderson, Feldblum, Modlin, Schirmacher, Schirmacher, Thandi — "A Practitioner's Guide to Generalized Linear Models") with R code. Python's statsmodels and scikit-learn libraries cover GLM and ML modeling. For smaller teams, carriers, and actuarial consulting firms, open-source tools plus Claude for documentation is a viable full-stack pricing workflow.

Where Claude Fits in the Pricing Workflow

Claude is not a pricing calculation engine — it does not fit GLMs, run development triangles, or execute XGBoost training runs. The pricing calculation happens in R, Python, or a platform like Radar or SAS. Claude's role is at the reasoning, review, and documentation layers that sit around the model:

• Assumption review. Paste trend assumptions, credibility weights, and factor selections — Claude evaluates whether the assumptions are directionally sensible, flags logical inconsistencies, and identifies which assumptions a state regulator is likely to challenge.
• Rate filing narrative. Claude drafts the actuarial rationale sections of a state rate filing — trend selection justification, credibility procedure description (ASOP No. 25), territory relativity justification, and response to department data requests. This is the highest-leverage use: the analysis takes hours, the documentation used to take hours more.
• Regulator response drafting. When a state insurance department issues a comment letter on a rate filing, Claude drafts the actuarial response — technical, ASOP-aware language that addresses each department comment specifically.
• Competitor Schedule P benchmarking. Claude reads competitor Schedule P data, identifies pricing trend divergence, and produces a benchmarking summary for the pricing committee.
• Pricing adequacy monitoring. Paste earned premium, incurred loss, and exposure data by territory and coverage — Claude identifies deteriorating loss ratios, flags where current rates appear inadequate given trend, and quantifies the indicated rate change per segment.

ASOP Compliance in AI-Assisted Actuarial Pricing

Using AI tools in actuarial pricing work raises specific ASOP compliance considerations that differ from reserving. The relevant standards are:

• ASOP No. 12 (Risk Classification). Governs the use of risk classification systems in pricing. Any rating variable — including ML-derived scores — must be actuarially justified and not unfairly discriminatory. If Claude helps draft the justification for a new rating variable, the actuary is responsible for verifying that the underlying analysis meets ASOP No. 12 requirements.
• ASOP No. 25 (Credibility Procedures). Requires that actuaries select credibility procedures appropriate to the situation and document their selection. Claude can help draft the credibility disclosure paragraph, but the actuary selects the procedure and verifies the calculation.
• ASOP No. 41 (Actuarial Communications). Requires identification of significant assumptions and methods. An actuarial report that references Claude-drafted narrative must still accurately describe the methods and assumptions that the actuary used — Claude writes the draft, the actuary verifies and certifies every assertion.

The practical compliance posture: using Claude to accelerate actuarial documentation is treated as writing assistance (like using prior-year templates) rather than as a change in methodology or a new reliance source. The AAA and CAS are developing AI-specific actuarial practice guidance; pricing actuaries should monitor CAS Forum publications and AAA practice notes for updates.

Working Prompts for Pricing Actuaries

These prompts are designed for Claude.ai Pro with a Project context set up for your line of business and pricing methodology. Each produces a complete first draft that the pricing actuary reviews, edits, and certifies. Replace illustrative data with your actual figures.

• "Review these GLM relativity estimates from a personal auto bodily injury frequency model and identify any actuarial concerns. The model is a Poisson log-linear GLM with earned car-years as the offset. Relativities (base = territory 01, standard driver age 35–44, clean record, no prior claims): Territory: 01=1.00, 02=1.14, 03=0.89, 04=1.67, 05=0.71, 06=2.31 Driver age band: 16–24=2.18, 25–34=1.31, 35–44=1.00, 45–54=0.84, 55–64=0.79, 65+=1.23 Prior claims (0=base): 1 prior=1.44, 2 prior=2.11, 3+=2.94 Vehicle age (1–3 years=base): 4–6 years=0.91, 7–10 years=0.83, 11+ years=0.79 Evaluate: (1) Territory 06 at 2.31x — does this appear actuarially reasonable or might it reflect data sparsity? What data volume would you want to see before accepting a 2.31x relativity; (2) The oldest driver age band (65+) shows higher frequency than 55–64 (1.23 vs 0.79) — this is actuarially expected due to cognitive/reaction factors, but how would you address state regulatory concerns about age-based rating in states with senior citizen protections; (3) Vehicle age relativities declining monotonically — is this pattern consistent with expected loss experience, or does it suggest confounding with driver age or coverage selection; (4) Produce a summary of actuarial review findings suitable for the pricing committee presentation."
• "Calculate the overall rate change indication for commercial general liability, state of Illinois, policy year 2027. Data: Experience period: accident years 2022–2024, policy year basis, earned premium $34.7M, incurred loss + ALAE $21.8M (at current development) Development: AY 2022 fully developed (tail factor 1.000), AY 2023 factor 1.042, AY 2024 factor 1.189 Frequency trend: +3.4%/year (company experience, 3-year weighted, full credibility at 1,200+ claims/year; this segment has 1,850 claims/year) Severity trend: +7.8%/year (company experience, partially credible; blended 70% company / 30% ISO GL industry trend of +6.2%) Trend period: 3.5 years from average accident date (midpoint of experience) to average accident date of future policy period Expense load: 31.2% of premium (fixed expenses 14.8%, variable 16.4%) Target profit margin: 5.0% On-level factor: 1.067 (current rates are 6.7% above the experience period average) Calculate step-by-step: (1) develop each AY to ultimate; (2) apply the on-level factor; (3) apply frequency and severity trends separately over the 3.5-year trend period; (4) calculate the trended, developed loss ratio; (5) calculate the target loss ratio; (6) calculate the indicated rate change; (7) comment on whether the resulting indication is directionally consistent with the loss ratio trend observable in the raw experience data."
• "Draft the actuarial rationale section for a personal auto rate filing in the state of Texas for a +11.3% overall rate change. This section will be reviewed by the Texas Department of Insurance. Key facts: the indicated change is +11.3%; we are filing for exactly the indication. Three-year weighted frequency trend: +4.2%. Three-year weighted severity trend: +8.6%. Trend period: 4.0 years (experience midpoint 2023, future policy midpoint 2027). Primary severity drivers: medical cost inflation (CPI medical +6.4% in Texas, 2022–2024), bodily injury severity social inflation (jury awards +2.4 points above medical inflation in Harris County and Dallas County — document from ISO Advisory Loss Cost filing PA-TX-2025-18). Credibility: 28,400 claims in the experience period — fully credible at the CAS 90/5 standard. No credibility blending with ISO data was applied. Include: (1) opening paragraph summarizing the overall indication and filing request; (2) trend selection methodology section with frequency and severity trend justification, credibility assessment, and trend period calculation shown explicitly; (3) severity driver narrative explaining the medical and social inflation components and citing data sources; (4) expense load explanation; (5) closing paragraph on the reasonableness of the overall indication. Write in the formal, ASOP-compliant language appropriate for a state regulatory filing. Do not include any unsupported assertions — every claim must be derivable from the data I have provided."
• "Analyze this commercial auto liability rate adequacy situation and recommend a response strategy. Facts: current average filed rate is $1,847 per power unit. The actuarial indicated rate is $2,214 per power unit — a deficiency of 16.7% on filed rates. The indication is based on a 3-year experience period (2022–2024) with frequency trend +6.1%/year and severity trend +9.4%/year (combined pure premium trend +16.0%/year). The company's loss ratio for accident year 2024 is 84.2% (accident year basis), above the target of 61.5% (expense load 32.0%, target profit 6.5%). The previous rate action was +8.5% filed in January 2024, which was a partial response to the prior +14.2% indication. Analyze: (1) Calculate the cumulative rate deficiency assuming rate increases of 0%, 5%, 10%, and 15% annually over the next 3 years, assuming the loss trend continues at the same pace; (2) At what annual rate increase does the company recover to rate adequacy (loss ratio at target) within 3 years? Within 5 years? (3) What are the 3 primary regulatory and competitive risks of filing for the full +16.7% indication in a single filing action versus phasing it over 2 years; (4) Draft a 1-page pricing committee memo presenting the inadequacy situation, quantifying the risk of inaction, and recommending the preferred rate action with supporting rationale."
• "Review this actuarial pricing model for homeowners insurance and identify gaps in the rating plan that may explain the observed adverse loss ratio in high-value properties. Rating variables currently in the filed model: construction type (frame/masonry/superior), protection class (1–10), amount of insurance (AIC) band, age of home band, year built band, roof material. Observed loss ratios by AIC band, accident year 2024: below $500K AIC: 51.3% loss ratio; $500K–$1M AIC: 68.7% loss ratio; $1M–$2M AIC: 82.4% loss ratio; above $2M AIC: 97.1% loss ratio. Analyze: (1) The monotonically deteriorating loss ratio by AIC band suggests the current model is systematically underpricing high-value properties. Identify 5 rating variables not in the current model that actuarial research suggests predict homeowners severity in high-value properties — variables that should be considered for addition to the rating plan; (2) What is the most likely explanation for the current model's failure to capture high-value property risk: inadequate severity model, wrong distributional assumption, missing interaction with construction type, or selection bias in the insured population; (3) Draft the actuarial recommendation for the pricing committee, including: the empirical evidence of inadequacy by AIC band, the proposed plan to develop and file new rating variables, and interim rate action to mitigate the inadequacy while the new model is developed."

Building an Actuarial Pricing Workflow with Claude

For pricing actuaries who want to integrate Claude systematically, the recommended setup is a Claude.ai Pro Project with the following context saved:

• Portfolio composition: lines of business, states, approximate volume (earned premium and claim counts)
• Current filed rates by state and line of business (or index of current adequacy by segment)
• Recent trend selections with data sources and credibility assessment
• Relevant ASOPs in scope (No. 12, 25, 41, and any line-of-business specific standards)
• Regulatory context: which states are rate-prior approval vs. file-and-use vs. no-file, any pending department inquiries

With this context loaded, prompts become shorter and outputs become more precisely calibrated. Asking Claude to "draft the trend justification for the Texas filing" works because it already knows the trend selections, the credibility procedure used, and the filing target. The one-time investment in setting up the Project context pays off across every pricing task in that filing cycle.

For the hands-on prompts that apply these models to a live filing — GLM relativity review, rate indication exhibits, trend justification, and state rate filing narratives — see Actuarial Pricing Models & GLM Insurance Pricing with AI. For the IBNR chain-ladder methodology underlying development factor selection in the rate indication, see IBNR Calculation with Claude. For the broader actuarial tool landscape including reserving platforms and documentation tools, see Best AI Tools for Actuaries in 2026. For P&C loss reserving methodology in depth, see P&C Loss Reserving AI. For insurance-specific pricing model validation under SR 11-7 and AI Act requirements, see Finance AI Model Validation Framework.

Frequently Asked Questions

What is the difference between a GLM and a GBM in actuarial pricing?

A GLM (generalized linear model) is the regulatory-compliant standard for P&C ratemaking — it produces interpretable multiplicative relativities that actuaries can explain to state insurance regulators and file as a rating plan. A GBM (gradient boosting machine, including XGBoost) captures non-linear interactions that GLMs miss, producing better predictive accuracy on holdout data. In practice, actuaries use GLMs for the primary rating plan and regulatory filing, and GBMs to identify segments where the GLM systematically underpredicts or overpredicts — informing new rating variable proposals. GBMs are rarely filed directly because state insurance departments require actuaries to justify each rating factor individually, which is not possible with a black-box ensemble model.

How many claims do you need for a credible actuarial pricing model?

The CAS limited fluctuations credibility standard for frequency is approximately 1,082 expected claims at the 90/5 standard (90% probability of being within ±5% of the true mean). For severity, which has higher variance, full credibility requires approximately 16,000 to 68,000 claims depending on the coefficient of variation of the severity distribution — making full severity credibility unusual for most company subsets. Most ratemaking work involves some level of partial credibility blending, particularly for geographic subdivisions, newer coverage types, or specialty lines with limited claim counts. Bühlmann credibility is more sophisticated than limited fluctuations for multi-class credibility problems and is gaining adoption in commercial lines pricing.

Can Claude write actuarial rate filings?

Claude can draft the actuarial narrative sections of a rate filing — trend justification, credibility procedure description, territory relativity explanation, and response to state department data requests. The pricing actuary provides the calculations and assumptions; Claude drafts the regulatory-quality prose. The actuary reviews every assertion for accuracy before the filing is submitted. State insurance departments review the actuarial certification, which the filing actuary signs — Claude drafts the language, the actuary owns the certification. This is analogous to using prior-year filing templates: it accelerates the documentation without changing the professional responsibility.

What is Earnix and how does it relate to actuarial pricing?

Earnix is a pricing optimization platform that sits downstream of the actuarial technical price. The actuarial GLM produces the expected loss cost per risk (the technical price). Earnix takes this as input and optimizes the offered premium — the price actually charged to the customer — to maximize portfolio value given conversion elasticity, retention dynamics, regulatory constraints, and strategic growth targets. A pure technical price maximizes actuarial adequacy but ignores competitive dynamics; Earnix balances actuarial adequacy with business optimization. Earnix integrates with actuarial model outputs from R, Python, SAS, and actuarial platforms like Radar and Hyperion.