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What risk measures are time consistent for all filtrations?

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  • Samuel N. Cohen

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.

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  • Samuel N. Cohen, 2010. "What risk measures are time consistent for all filtrations?," Papers 1007.0610, arXiv.org.
    • Handle: RePEc:arx:papers:1007.0610
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    References listed on IDEAS

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    1. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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