Entropic risk measure

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. It is a possible alternative to other risk measures as value-at-risk or expected shortfall.

It is a theoretically interesting measure because it provides different risk values for different individuals whose attitudes toward risk may differ. 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. Given the connection to utility functions, it can be used in utility maximization problems.

The entropic risk measure with the risk aversion parameter ${\displaystyle \theta >0}$ is defined as

where ${\displaystyle H(Q|P)=E\left[{\frac {dQ}{dP}}\log {\frac {dQ}{dP}}\right]}$ is the relative entropy of Q << P.

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