An Offspring of Multivariate Extreme-Value Theory: The\n Max-Characteristic Function

2016/03/08 by Michael Falk, Falk, Michael, Gilles Stupfler +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G70 #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary 60E10 #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications #secondary 60F99

paper · pdf · doi:10.48550/arxiv.1603.02575

openalex publication_date 2016/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces max-characteristic functions (max-CFs), which are an\noffspring of multivariate extreme-value theory. A max-CF characterizes the\ndistribution of a random vector in R^d , whose components are nonnegative and\nhave finite expectation. Pointwise convergence of max-CFs is shown to be\nequivalent with convergence with respect to the Wasserstein metric. The space\nof max-CFs is not closed in the sense of pointwise convergence. An inversion\nformula for max-CFs is established.\n

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