In financial mathematics, the entropic risk measure is a risk measure which depends on the risk aversion of the user through the exponential utility function. This makes it a theoretically interesting measure because it would provide different risk values for different individuals. However, in practice it would be difficult to use since quantifying the risk aversion for an individual is difficult to do. The entropic risk measure is the prime example of a convex risk measure which is not coherent.[1] Given the connection to utility functions already, it is an obvious choice for the constraints in utility maximization problems.
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The entropic risk measure with parameter (the risk aversion parameter) is defined as
where is the relative entropy of Q << P.[3]
The acceptance set for the entropic risk measure is the set of payoffs with positive expected utility. That is
where is the exponential utility function.[3]
The conditional risk measure associated with dynamic entropic risk with risk aversion parameter is given by
This is a time consistent risk measure if is constant through time.[4]