RISK MEASURES FOR NON‐INTEGRABLE RANDOM VARIABLES

Freddy Delbaen

Mathematical Finance, 2009, vol. 19, issue 2, 329-333

Abstract: We show that when a real‐valued risk measure is defined on a solid, rearrangement invariant space of random variables, then necessarily it satisfies a weak compactness, also called continuity from below, property, and the space necessarily consists of integrable random variables. As a result we see that a risk measure defined for, say, Cauchy‐distributed random variable, must take infinite values for some of the random variables.

Date: 2009
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