Bühlmann--Straub (B-S) credibility assigns each account a weight $Z_i = E_i/(E_i+K)$, where $K$ is a single portfolio-wide ratio. The formula assumes $K$ is the same for every account regardless of size, history length, or volatility, and that recent and older years carry equal weight. On a held-out US commercial auto dataset these assumptions fail: standard B-S applied to 96 companies produces a calibration slope of 29 for small accounts, a signature of severe under-crediting. We propose a joint framework that retains B-S interpretability while addressing these limitations. The credibility weight $Z_i$ is modelled as a logistic function of account characteristics; historical experience is discounted by an EWMA decay parameter $λ$ estimated from the data; and $Z$, $λ$, and the complement are optimised in a single likelihood pass. The framework formally nests Bühlmann--Straub as a special case, admitting a likelihood-ratio test for any proposed extension. On a two-year held-out test set the proposed model restores calibration (slope = 1.00) and reduces exposure-weighted prediction error by 38% (90% bootstrap interval: 26%--50%). A size gradient in the decay rate emerges ($\hatλ\approx 0.6$, $0.84$, $0.13$ for Small, Mid, Large) and replicates qualitatively on Other Liability. A simulation study confirms the mechanisms. The model requires only account-year summaries and delivers three transparent outputs: credibility weight, complement, and recommended renewal rate.

翻译：Bühlmann–Straub（B-S）可信度模型为每个账户赋予权重 $Z_i = E_i/(E_i+K)$，其中 $K$ 是整个投资组合的单一比率。该公式假设 $K$ 对所有账户（无论规模、历史长度或波动性）均相同，且近期与早期年份具有同等权重。在保留的美国商业汽车数据集上，这些假设失效：对96家公司应用标准B-S模型导致小账户的校准斜率为29，这是严重低可信度的标志。本文提出一个联合框架，在保留B-S模型可解释性的同时解决上述局限性。该框架将可信度权重 $Z_i$ 建模为账户特征的逻辑函数；通过数据估计的指数加权移动平均（EWMA）衰减参数 $λ$ 对历史经验进行折现；并采用单次似然优化过程同时求解 $Z$、$λ$ 及其互补参数。该框架在形式上嵌套Bühlmann–Straub模型作为特例，允许通过似然比检验验证任何扩展方案。在两年保留测试集上，所提模型恢复了校准特性（斜率=1.00），并将暴露加权预测误差降低38%（90%自助法置信区间：26%-50%）。衰减率呈现规模梯度（小型、中型、大型账户的$\hatλ$值分别为0.6、0.84、0.13），该模式在《其他责任险》数据中得到定性复现。仿真实验验证了相关机制。该模型仅需账户-年度汇总数据，输出三个透明指标：可信度权重、互补参数及建议续期费率。