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A coherent risk measure is a function that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance. Properties.
The former definition may not be a coherent risk measure in general, however it is coherent if the underlying distribution is continuous. [4] The latter definition is a coherent risk measure. [3] TVaR accounts for the severity of the failure, not only the chance of failure. The TVaR is a measure of the expectation only in the tail of the ...
Risk measure. Distortion risk measure; Tail conditional expectation; Value at risk; Convex risk measure Entropic risk measure; Coherent risk measure. Discounted maximum loss; Expected shortfall; Superhedging price; Spectral risk measure; Deviation risk measure. Standard deviation or Variance; Mid-range Interdecile range; Interquartile range
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A risk measure is defined as a mapping from a set of random variables to the real numbers. This set of random variables represents portfolio returns. The common notation for a risk measure associated with a random variable X {\displaystyle X} is ρ ( X ) {\displaystyle \rho (X)} .
A coherent risk measure satisfies the following four properties: 1. Subadditivity. A risk measure is subadditive if for any portfolios A and B, the risk of A+B is never greater than the risk of A plus the risk of B. In other words, the risk of the sum of subportfolios is smaller than or equal to the sum of their individual risks.
Many risk measures have hitherto been proposed, each having certain characteristics. The entropic value at risk (EVaR) is a coherent risk measure introduced by Ahmadi-Javid, [1] [2] which is an upper bound for the value at risk (VaR) and the conditional value at risk (CVaR), obtained from the Chernoff inequality. The EVaR can also be ...
Amazon stock was clipped by 3% to $231.80 each in premarket trading on Friday after the tech giant delivered mixed first quarter guidance and promised big spending on AI infrastructure in 2025.