Do law-invariant linear functionals collapse to the mean?

2021/07/23 by Shengzhong Chen, Chen, Shengzhong, Niushan Gao +5
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #46E30 #60E05 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2107.11239

openalex publication_date 2021/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we show that, on a wide range of rearrangement-invariant spaces, a law-invariant bounded linear functional is a scalar multiple of the expectation. We also construct a rearrangement-invariant space on which this property fails.

Citations

• The strong Fatou property of risk measures

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