Mathematical definition
A function , where is the L2 space of random variables (random portfolio returns), is a deviation risk measure if
In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measures generalize the concept of standard deviation.
A function , where is the L2 space of random variables (random portfolio returns), is a deviation risk measure if
There is a one-to-one relationship between a deviation risk measure D and an expectation-bounded risk measure R where for any
R is expectation bounded if for any nonconstant X and for any constant X.
If for every X (where is the essential infimum), then there is a relationship between D and a coherent risk measure. [1]
The most well-known examples of risk deviation measures are: [1]
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