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.
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
e s s inf
e s s inf
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]