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Risk measures [25]

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Bullet points include: Artzner et al. (1999) also showed that a risk measure is coherent if and only if there is a family, F, of probability measures, P, such that. Sometimes easiest way to prove that a risk measure is coherent is to prove each of the four axioms are satisfied, at other times it is easiest to show that it may be expressed in this supremum form. E.g. TVaR is coherent. Define family of probability measures (indexed by n = number of observations) placing equal prob on k realisations, where k = largest integer such that k/n <alpha. TVaR is then max expected value of losses over this family of distributions as n tends to infinity

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