发表机构
Microprediction（Microprediction）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明嵌套聚类优化是Schur桥的一端，并给出在估计误差下内部点（部分耦合）可严格优于端点，且提供精确示例与闭式解。
AI 中文摘要
嵌套聚类优化在每一簇内使用该簇自身的协方差块进行配置，然后对所得的簇级投资组合进行跨簇配置。块求逆表明，无约束的最小方差投资组合具有相同的两层结构，其中每个块被替换为其相对于其他所有资产的Schur补。相反，若以每个其他簇中的一个节点为条件，则按Vecchia近似的方式截断条件集，我们给出了在此条件下跨簇依赖的秩一模型，该模型下此截断是精确的。将补项乘以γ∈[0,1]进行阻尼，便得到一座桥：γ=0时为嵌套聚类优化，γ=1时为全局最优，且无需进行大于簇规模或簇数量的线性求解。在估计误差下，最优γ可以严格位于内部，而完全耦合也可能保持最优；我们给出了最小方差端点的局部定理，并提供了两者的精确示例，其中包括一个对称族，其最优解为闭式形式。
英文摘要
Nested clustered optimization allocates within each cluster from the cluster's own covariance block and then across the resulting cluster portfolios. Block inversion says the unconstrained minimum-variance portfolio has the same two-tier shape, with each block replaced by its Schur complement against every other asset. Conditioning instead on one knot from each other cluster truncates the conditioning set in the manner of a Vecchia approximation, and we give the rank-one model of cross-cluster dependence under which it is exact. Damping the complement by $γ\in[0,1]$ then gives a bridge with nested clustered optimization at $γ=0$ and the global optimum at $γ=1$, with no linear solve larger than a cluster or the number of clusters. Under estimation error the optimal $γ$ can be strictly interior and full coupling can remain optimal, and we give the local theorem at the minimum-variance end with exact examples of both, including a symmetric family in which the optimum is a closed form.
