发表机构
Université du Québec à Montréal; Kyoto University; Chaire PARI (Institut Europlace de Finance–ILB, ENSAE Paris & Sciences Po); Institut Europlace de Finance–ILB; ENSAE Paris; Sciences Po（魁北克大学蒙特利尔分校; 京都大学; PARI讲席（欧洲金融中心研究所-ILB，巴黎国立统计与经济管理学院与巴黎政治学院）; 欧洲金融中心研究所; 巴黎国立统计与经济管理学院; 巴黎政治学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出基准相对池化-分层尺度，量化保险定价中池化与差异化的权衡，并揭示费率调整对边际差异化、分配及转移的不同影响。
AI 中文摘要
保险定价将池化与差异化相结合：费率表可能将预期损失的基准差异部分互济化，或将其转化为保单层面的保费差异。我们提出了一个具有两个互补坐标的基准相对池化-分层尺度。耦合的$L^p$坐标衡量评估费率表与既定基准纯保费之间的保单层面一致性，而边际Wasserstein坐标则比较其暴露加权保费分布。两者残差$p$-成本之差定义了分配错配。在投资组合平衡下，耦合的$L^1$坐标具有精确的精算解释：它是费率表所移除的完全池化引起的转移量的比例。合成和汽车保险应用表明，广泛类别、代理变量、收缩和尾部上限可能对边际差异化、保单层面分配和转移产生不同影响。一个重心群体平价干预进一步表明，条件保费差异可能主要通过重新分配和恢复基准相对转移而下降，而边际差异化变化很小。
英文摘要
Insurance pricing combines pooling with differentiation: a tariff may leave benchmark differences in expected loss partly mutualized or translate them into policy-level premium differences. We propose a benchmark-relative pooling--profiling scale with two complementary coordinates. The coupled $L^p$ coordinate measures policy-level alignment between an evaluated tariff and a stated benchmark pure premium, whereas the marginal Wasserstein coordinate compares their exposure-weighted premium distributions. The difference between their residual $p$-costs defines an allocation mismatch. Under portfolio balance, the coupled $L^1$ coordinate has an exact actuarial interpretation: it is the fraction of the transfer volume induced by full pooling that the tariff removes. Synthetic and motor-insurance applications show that broad classes, proxies, shrinkage and tail caps can affect marginal differentiation, policy-level allocation and transfers differently. A barycentric group-parity intervention further shows that conditional premium disparities can fall mainly through reallocation and restored benchmark-relative transfers, with little change in marginal differentiation.
