A simple characterization of tightness for convex solid sets of positive random variables

Pablo Koch-Medina; Cosimo Munari; Mario Šikić

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arXiv · 1704.00257

A simple characterization of tightness for convex solid sets of positive random variables

Pablo Koch-Medina·Cosimo Munari·Mario Šikić

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Abstract

We show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient that it is radially bounded, i.e. that every ray passing through one of its elements eventually leaves the set. The result is motivated by problems arising in mathematical finance.

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Pablo Koch-Medina, Cosimo Munari, Mario Šikić. 2017-04-02. A simple characterization of tightness for convex solid sets of positive random variables. https://arxiv.org/abs/1704.00257

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