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 to be 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.
A simple characterization of tightness for convex solid sets of positive random variables
Munari, C;
2018-01-01
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 to be 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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