A structural characterization of numeraires of convex sets of nonnegative random variables

2010/03/29 by Constantinos Kardaras, Kardaras, Constantinos
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #46A16 #46E30 #60A10 #Economic theories and models #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.FA #math.PR #msc:46A16 #msc:46E30 #msc:60A10

paper · pdf · doi:10.48550/arxiv.1003.5419

8 pages; final version

openalex publication_date 2010/03/29 · arxiv created 2011/03/18 · arxiv updated 2011/03/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We introduce the concept of numeraires of convex sets in the nonnegative orthant of the topological vector space of all random variables built over a probability space. A necessary and sufficient condition for an element of a convex set to be its numeraire is given, inspired from ideas in financial mathematics.

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