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What risk measures are time consistent for all filtrations? (1007.0610v1)

Published 5 Jul 2010 in q-fin.RM and math.PR

Abstract: We study coherent risk measures which are time-consistent for multiple filtrations. We show that a coherent risk measure is time-consistent for every filtration if and only if it is one of four main types. Furthermore, if the risk measure is strictly monotone it is linear, and if the reference probability space is not atomic then it is either linear or an essential supremum.