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arxiv: 2606.29371 · v1 · pith:U4YRYUERnew · submitted 2026-06-28 · 📊 stat.AP

Semantic insurance pricing with large language models

Christopher Blier-Wong , Derek Kusmenko This is my paper

Pith reviewed 2026-06-30 02:10 UTC · model grok-4.3

classification 📊 stat.AP
keywords insurance pricinglarge language modelsembeddingsgeneralized linear modelsclaim frequencyactuarial modelingPoisson regressionFrench motor data
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The pith

Embeddings from a pre-trained large language model can replace hand-crafted features as inputs to a standard actuarial pricing model for Poisson claim-frequency regression.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines whether embeddings computed from natural-language policyholder descriptions can substitute for manually engineered risk factors in classical insurance pricing. On French motor third-party liability data the embedding inputs fed into a generalized linear model yield lower prediction error than the usual hand-crafted features, with the largest gains appearing when the training sample is small. At bigger sample sizes the advantage becomes sensitive to model choice and embedding dimension. The authors also show that domain-specific fine-tuning of the embeddings helps and that the pipeline changes output when any out-of-template text is added to the prompt.

Core claim

Embeddings from a pre-trained large language model, computed from a natural-language description of each policyholder, can replace hand-crafted features as inputs to a standard actuarial pricing model. Using French motor third-party liability data the embedding-based model outperforms the generalized linear model, especially when data are scarce, whereas at larger sample sizes the comparison is model- and dimension-dependent. Insurance-specific fine-tuning further improves the embeddings, and a prompt-sensitivity diagnostic shows that the pipeline reacts to any appended out-of-template field, making controlled prompts a governance requirement.

What carries the argument

Pre-trained language-model embeddings treated as fixed covariates inside a generalized linear model for Poisson claim-frequency regression.

Load-bearing premise

The supplied natural-language policy descriptions already contain the risk-relevant information that the embeddings extract without systematic bias or loss of actuarial signal.

What would settle it

A new motor-insurance dataset in which the embedding-based generalized linear model shows no improvement over the hand-crafted-feature version on small training samples would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2606.29371 by Christopher Blier-Wong, Derek Kusmenko.

Figure 1
Figure 1. Figure 1: Overview of the embedding-based pricing pipeline: structured covariates are serialized into [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Default instruction-prefixed underwriting-list prompt for generating LLM embeddings [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Learning curves comparing the baseline GLM (48 hand-engineered features) against [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of embedding dimension and reduction method on test deviance across embedding [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Test mean Poisson deviance for two ways of combining Qwen embeddings with the [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows the main effect of fine-tuning for the two strongest adapters in the evaluated grid. Fine-tuning shifts the Qwen PCA curve downward at every tested dimension, with the largest gain at K = 48. The 100,000-pair, two-epoch adapter provides the strongest low-dimensional embedding-only result, while the 200,000-pair, two-epoch adapter gives the best high-dimensional result. Adding the raw GLM covariates t… view at source ↗
Figure 7
Figure 7. Figure 7: Learning curves for Qwen fine-tuning at K = 48. The left panel shows the full range from n = 1,000 to n = 500,000; the right panel zooms in on the stable medium- and large-sample regime. Raw-plus-LoRA appends the 48 GLM covariates to the 48 fine-tuned PCA components. The 100,000-pair and 200,000-pair adapters shown are the two-epoch variants, matching the labelling of [PITH_FULL_IMAGE:figures/full_fig_p02… view at source ↗
Figure 8
Figure 8. Figure 8: Distribution summaries of individual-level predicted frequency shifts for the five prompt [PITH_FULL_IMAGE:figures/full_fig_p031_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: UMAP projection of the Qwen3-Embedding-0.6B policyholder embeddings, colored by [PITH_FULL_IMAGE:figures/full_fig_p032_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Per-band feature profile. Each cell prints the mean of that feature over the policies in the [PITH_FULL_IMAGE:figures/full_fig_p033_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Exposure-weighted claim frequency by band, computed on the full [PITH_FULL_IMAGE:figures/full_fig_p034_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Prose narrative prompt. The prose format ( [PITH_FULL_IMAGE:figures/full_fig_p035_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Minimal key-value prompt. The minimal format ( [PITH_FULL_IMAGE:figures/full_fig_p036_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Task-instruction list prompt. This format ( [PITH_FULL_IMAGE:figures/full_fig_p036_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Qualitative descriptor prompt. This format ( [PITH_FULL_IMAGE:figures/full_fig_p037_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Long underwriting prompt. The long underwriting prompt ( [PITH_FULL_IMAGE:figures/full_fig_p038_16.png] view at source ↗
read the original abstract

Classical actuarial pricing models, such as the generalized linear model, are valued for transparency and ease of governance, but they use interactions among risk factors only when these are supplied through explicit feature engineering. We study whether embeddings from a pre-trained large language model, computed from a natural-language description of each policyholder, can replace hand-crafted features as inputs to a standard actuarial pricing model, taking Poisson claim-frequency regression as the main example. The language model is used only to construct deterministic embedding covariates; pricing is performed by a standard generalized linear model. Using French motor third-party liability data, the embedding-based model outperforms the generalized linear model, especially when data are scarce, whereas at larger sample sizes the comparison is model- and dimension-dependent. Insurance-specific fine-tuning further improves the embeddings, and a prompt-sensitivity diagnostic shows that the pipeline reacts to any appended out-of-template field, making controlled prompts a governance requirement.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes replacing hand-crafted features with deterministic embeddings from a pre-trained LLM applied to natural-language policyholder descriptions as covariates in a standard GLM for Poisson claim-frequency regression. On French motor third-party liability data, the embedding-based GLM outperforms the baseline GLM (especially in low-data regimes), with further gains from insurance-specific fine-tuning; a prompt-sensitivity check indicates the need for controlled prompts.

Significance. If the performance gains are robust and attributable to extractable actuarial signal in the text, the approach offers a way to incorporate unstructured data into transparent, governance-friendly pricing models without abandoning GLMs. The deterministic embedding step and retention of the GLM are strengths that keep the method within existing actuarial workflows. The low-data regime result, if confirmed with proper controls, would be particularly relevant for new lines or small portfolios.

major comments (2)
  1. [Abstract, §3] Abstract and §3 (data description): the central claim that embeddings 'can replace hand-crafted features' and outperform them rests on the assumption that the natural-language descriptions encode risk-relevant information not already captured by the baseline covariates. The manuscript provides no details on whether these descriptions are free-form applicant text, templated conversions of the structured fields, or richer external text; without this, outperformance cannot be unambiguously attributed to semantic extraction rather than implicit non-linear feature engineering or data leakage.
  2. [§4] §4 (experimental results): the abstract states outperformance 'especially when data are scarce' and 'model- and dimension-dependent' at larger sizes, yet the provided text contains no quantitative metrics, confidence intervals, data-split details, or statistical significance tests. This absence makes the load-bearing empirical claim unverifiable from the given information and requires explicit tables or figures with effect sizes.
minor comments (2)
  1. [Abstract] Abstract: the claim of outperformance should be accompanied by at least one quantitative metric (e.g., relative improvement in Poisson deviance or log-likelihood) even in the abstract.
  2. [§2] Notation: clarify whether the GLM is fit on the raw embeddings or on a reduced-dimensional projection, and state the exact dimension choice and any regularization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important areas for clarification and strengthening of the empirical presentation. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract, §3] Abstract and §3 (data description): the central claim that embeddings 'can replace hand-crafted features' and outperform them rests on the assumption that the natural-language descriptions encode risk-relevant information not already captured by the baseline covariates. The manuscript provides no details on whether these descriptions are free-form applicant text, templated conversions of the structured fields, or richer external text; without this, outperformance cannot be unambiguously attributed to semantic extraction rather than implicit non-linear feature engineering or data leakage.

    Authors: We agree that the source and construction of the natural-language descriptions must be specified to support attribution of performance gains to semantic content rather than leakage or implicit engineering. In the revised manuscript we will expand the data description in §3 to state explicitly how the descriptions are obtained (free-form applicant text versus any templating or conversion from structured fields) and will add a short discussion of how this affects interpretation of the results. revision: yes

  2. Referee: [§4] §4 (experimental results): the abstract states outperformance 'especially when data are scarce' and 'model- and dimension-dependent' at larger sizes, yet the provided text contains no quantitative metrics, confidence intervals, data-split details, or statistical significance tests. This absence makes the load-bearing empirical claim unverifiable from the given information and requires explicit tables or figures with effect sizes.

    Authors: We accept that the current manuscript version does not present the quantitative results with sufficient detail for independent verification. In the revision we will add tables and figures in §4 that report the relevant performance metrics together with confidence intervals, explicit data-split and cross-validation procedures, and statistical significance tests comparing the embedding-based and baseline GLMs. revision: yes

Circularity Check

0 steps flagged

No circularity: direct empirical comparison of covariate sets in standard GLM

full rationale

The paper's central claim is an empirical performance comparison: LLM embeddings computed from natural-language policy descriptions are substituted as covariates into an otherwise standard Poisson GLM and evaluated against a baseline GLM using hand-crafted features on French motor data. No equations, uniqueness theorems, or predictions are derived; the pipeline is a deterministic embedding step followed by off-the-shelf GLM fitting and out-of-sample evaluation. No self-citations are load-bearing for the result, no fitted parameters are relabeled as predictions, and no ansatz is smuggled via prior work. The derivation chain is self-contained against external benchmarks and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the assumption that LLM embeddings preserve actuarial signal from text without post-hoc selection or bias; no free parameters, axioms, or invented entities are explicitly introduced beyond standard GLM and pre-trained model usage.

pith-pipeline@v0.9.1-grok · 5676 in / 1092 out tokens · 23533 ms · 2026-06-30T02:10:17.663787+00:00 · methodology

discussion (0)

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Reference graph

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