Isotonic Recalibration under a Low Signal-to-Noise Ratio

TL;DR

This paper introduces isotonic recalibration for regression models in insurance pricing, ensuring auto-calibration and interpretability especially under low signal-to-noise conditions.

Contribution

It demonstrates that isotonic recalibration guarantees auto-calibration and results in low-complexity, explainable pricing functions in low signal-to-noise scenarios.

Findings

Recalibrated models are auto-calibrated.

Recalibrated functions have low complexity.

Effective under low signal-to-noise ratio.

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.