We study the aggregate hazard rate of a heterogeneous population whose individual event intensities are modeled as Cox (doubly stochastic) processes. In the deterministic hazard setting, the observed pool hazard is the survival weighted mean of the individual hazards, and its time derivative equals the mean individual hazard drift minus a variance term. This yields a transparent structural explanation of burnout in mortgage pools. We extend this perspective to stochastic intensity models. The observed pool hazard remains a survival-weighted mean, but now evolves as an Ito process whose drift contains the mean drift of the individual hazards and a negative selection term driven by cross-sectional dispersion, together with a diffusion term inherited from the common factor. We formulate the general identity and discuss special cases relevant to mortgage prepayment modeling.

翻译：本研究探讨了个体事件强度建模为Cox（双重随机）过程的异质群体聚合风险率。在确定性风险设定中，观测池风险率为个体风险率的生存加权均值，其时间导数等于个体风险率漂移项的均值减去方差项。这为抵押贷款池中的耗竭现象提供了清晰的结构性解释。我们将此视角扩展至随机强度模型。观测池风险率仍保持为生存加权均值，但现演化为伊藤过程，其漂移项包含个体风险率的平均漂移量及由横截面离散度驱动的负向选择项，同时包含从共同因子继承的扩散项。我们建立了普适恒等式，并讨论了与抵押贷款提前还款建模相关的特殊情形。