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：我们研究了一类异质性总体中的聚集危险率，其中个体事件强度被建模为Cox（双重随机）过程。在确定性危险设定下，观测到的池危险是个体危险经生存加权的均值，其时间导数等于个体危险漂移均值减去一个方差项。这为抵押贷款池中的耗竭现象提供了透明的结构性解释。我们将这一视角扩展到随机强度模型。观测到的池危险仍保持为生存加权均值，但此时作为伊藤过程演化，其漂移包含个体危险漂移均值与由横截面离散性驱动的负向选择项，以及来自共同因子的扩散项。我们建立了该一般恒等式，并讨论了与抵押贷款提前偿付建模相关的特例。