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.

翻译：本文首次建立了预测模型性能与保险定价中损失率之间的解析关系。我们推导了一个闭式公式，将预测损失与实际损失之间的皮尔逊相关系数与预期损失率联系起来。该框架证明模型改进具有边际收益递减的特性，从解析角度确认了应优先改进性能较差模型的精算直觉。我们引入了损失率误差度量，用于量化频率、严重性和纯保费模型的业务影响。仿真结果表明，在给定假设下预测可靠，且在假设违反时呈现优雅退化。该框架将模型投资决策从定性直觉转变为定量成本效益分析。