A Theoretical Framework Bridging Model Validation and Loss Ratio in Insurance

TL;DR

This paper develops a theoretical framework linking predictive model performance to loss ratio in insurance, enabling quantitative assessment of model improvements and their business impact.

Contribution

It introduces an analytical relationship between model accuracy and loss ratio, including a new Loss Ratio Error metric for comprehensive business impact evaluation.

Findings

Derived a closed-form formula relating Pearson correlation to loss ratio

Confirmed diminishing returns in model improvements

Validated the framework through simulations showing reliable predictions

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.