Isotonic Recalibration under a Low Signal-to-Noise Ratio

Paper: arXiv 2301.02692

Authors: Mario V. Wüthrich, Johanna Ziegel

Abstract

Insurance pricing systems should fulfill the auto-calibration property to ensure that there is no systematic cross-financing between different price cohorts. Often, regression models are not auto-calibrated. We propose to apply isotonic recalibration to a given regression model to ensure auto-calibration. Our main result proves that under a low signal-to-noise ratio, this isotonic recalibration step leads to explainable pricing systems because the resulting isotonically recalibrated regression functions have a low complexity.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically sound theoretical framework proving that isotonic recalibration reduces model complexity under low signal-to-noise ratios. However, it leans heavily on theoretical proofs with limited empirical backtesting and real-world data validation presented in the excerpt.

Research Flowchart

  flowchart TD
    A[Goal: Ensure Auto-Calibration & Explainability in Insurance Pricing] --> B[Input: Base Regression Model with Non-Auto-Calibrated Predictions]
    B --> C[Method: Apply Isotonic Recalibration]
    C --> D[Process: Non-Parametric Monotonic Optimization under Low SNR]
    D --> E[Outcome 1: Auto-Calibrated Pricing System]
    D --> F[Outcome 2: Reduced Model Complexity & Higher Explainability]