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

2017/04/02 by Pablo Koch‐Medina, Koch-Medina, Pablo, Cosimo Munari +3
Decision Sciences · Economics, Econometrics and Finance · #46A16 #46E30 #60A10 #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1704.00257

openalex publication_date 2017/04/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We show that for a convex solid set of positive random variables to be tight,\nor equivalently bounded in probability, it is necessary and sufficient that it\nis radially bounded, i.e. that every ray passing through one of its elements\neventually leaves the set. The result is motivated by problems arising in\nmathematical finance.\n

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