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Abstract
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In the first partof the talk I shall survey the basic facts about coherent and convex risk measures (in the contexts of the talk the risk measures are a class of some non-linear functionals on the space of uniformly bounded random variables).
Second part of the talk will be devoted to the recent result of A.Cherny and P.Grigoriev, who proved that on an atomless probability space a risk measure is law invariant iff it is dilatation monotone (i.e. monotone with respect to the conditional expectations over all sigma-subalgebras). In some sense this result could be viewed as an inverse theorem to the characterization of the law-invariant risk measures due to Kusuoka and Follmer and Schied.
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