Search results
Results from the WOW.Com Content Network
The tail value at risk (or tail conditional expectation) is a coherent risk measure only when the underlying distribution is continuous. The Wang transform function (distortion function) for the tail value at risk is g ( x ) = min ( x α , 1 ) {\displaystyle g(x)=\min({\frac {x}{\alpha }},1)} .
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 ...
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions , such as banks and insurance companies, acceptable to the regulator .
In financial mathematics and stochastic optimization, the concept of risk measure is used to quantify the risk involved in a random outcome or risk position. 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 ...
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
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.
An acceptance set is convex (coherent) if and only if the corresponding risk measure is convex (coherent). As defined below it can be shown that () = ...
A spectral risk measure is always a coherent risk measure, but the converse does not always hold. An advantage of spectral measures is the way in which they can be related to risk aversion, and particularly to a utility function, through the weights given to the possible portfolio returns. [1]