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Stochastic orders and risk measures: Consistency and bounds

By Nicole Bäuerle and Alfred Müller


We investigate the problem of consistency of risk measures with respect to usual stochastic order and convex order. It is shown that under weak regularity conditions risk measures are consistent with these stochastic orders. This result is used to derive bounds for risk measures of portfolios. As a by-product, we extend the characterization of Kusuoka (2001) of coherent, law-invariant risk measures with the Fatou property to unbounded random variables

Topics: coherent risk measure, convex risk measure, stochastic order
Year: 2005
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