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math.ST2020
On characteristic rank for matrix and tensor completion
Alexander Shapiro, Yao Xie, Rui Zhang
In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of…
math.ST2012★ 10 cited
Uniqueness of Kusuoka Representations
Alois Pichler, Alexander Shapiro
This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka rep…