Paper: arXiv 2512.03242

Authors: C. Evans Hedges

Abstract

This paper establishes the first analytical relationship between predictive model performance and loss ratio in insurance pricing. We derive a closed-form formula connecting the Pearson correlation between predicted and actual losses to expected loss ratio. The framework proves that model improvements exhibit diminishing marginal returns, analytically confirming the actuarial intuition to prioritize poorly performing models. We introduce the Loss Ratio Error metric for quantifying business impact across frequency, severity, and pure premium models. Simulations show reliable predictions under stated assumptions, with graceful degradation under assumption violations. This framework transforms model investment decisions from qualitative intuition to quantitative cost-benefit analysis.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical bridge between statistical model performance metrics (Pearson correlation) and actual business outcomes (loss ratio) via clear analytical proofs. While mathematically sound and exceptionally clear, it relies heavily on synthetic grid simulations rather than extensive empirical backtests on real-world insurance datasets.

Research Flowchart

  flowchart TD
    A["<b>Research Goal</b><br>Quantify link between predictive model<br>performance & expected loss ratio"] --> B["<b>Inputs & Models</b><br>Frequency, Severity, Pure Premium<br>predictions vs. actual losses"]
    
    B --> C["<b>Analytical Framework</b><br>Derive closed-form formula via Pearson<br>correlation between predicted & actuals"]
    
    C --> D["<b>Validation & Testing</b><br>Simulations testing core assumptions<br>& graceful degradation"]
    
    D --> E["<b>New Metric: Loss Ratio Error</b><br>Quantifies direct financial/business impact"]
    
    E --> F["<b>Key Outcomes</b><br>• Proves diminishing returns on model tuning<br>• Confirms prioritizing weak models<br>• Enables quantitative ROI for model investments"]

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0 of 57 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.