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

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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.

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  1. Mathematics and Statistics Department, Boston University, 111 Cummington Street, Boston, MA, 02215, USA

    Constantinos Kardaras

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  1. Constantinos Kardaras
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Correspondence to Constantinos Kardaras.

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C. Kardaras acknowledges partial support by the National Science Foundation, under award number DMS-0908461. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect those of the National Science Foundation.

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Kardaras, C. A structural characterization of numéraires of convex sets of nonnegative random variables. Positivity 16, 245–253 (2012). https://doi.org/10.1007/s11117-011-0120-1

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  • DOI: https://doi.org/10.1007/s11117-011-0120-1

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