# A structural characterization of numéraires of convex sets of nonnegative random variables

A structural characterization of numéraires of convex sets of nonnegative random variables We introduce the concept of numéraire s of convex sets in $${L^0_{+}}$$ , the nonnegative orthant of the topological vector space L 0 of all random variables built over a probability space. A necessary and sufficient condition for an element of a convex set $${\mathcal{C} \subseteq L^0_{+}}$$ to be a numéraire of $${\mathcal{C}}$$ is given, inspired from ideas in financial mathematics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# A structural characterization of numéraires of convex sets of nonnegative random variables

Positivity, Volume 16 (2) – Apr 16, 2011
9 pages

/lp/springer_journal/a-structural-characterization-of-num-raires-of-convex-sets-of-Z3ihylTTzU
Publisher
Springer Journals
Copyright © 2011 by Springer Basel AG
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Fourier Analysis; Operator Theory; Econometrics; Potential Theory
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-011-0120-1
Publisher site
See Article on Publisher Site

### Abstract

We introduce the concept of numéraire s of convex sets in $${L^0_{+}}$$ , the nonnegative orthant of the topological vector space L 0 of all random variables built over a probability space. A necessary and sufficient condition for an element of a convex set $${\mathcal{C} \subseteq L^0_{+}}$$ to be a numéraire of $${\mathcal{C}}$$ is given, inspired from ideas in financial mathematics.

### Journal

PositivitySpringer Journals

Published: Apr 16, 2011

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