In financial mathematics (concerned with mathematical modeling of financial markets), 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.
The entropic risk measure is the prime example of a convex risk measure which is not coherent.
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.
is given by This is a time consistent risk measure if
is constant through time, [4] and can be computed efficiently using forward-backwards differential equations[5] [6] .