In probability theory, the minimal-entropy martingale measure (MEMM) is the risk-neutral probability measure that minimises the entropy difference between the objective probability measure,
In incomplete markets, this is one way of choosing a risk-neutral measure (from the infinite number available) so as to still maintain the no-arbitrage conditions.
The MEMM has the advantage that the measure
Another common choice of equivalent martingale measure is the minimal martingale measure, which minimises the variance of the equivalent martingale.
For certain situations, the resultant measure
In a finite probability model, for objective probabilities
then one must minimise the Kullback–Leibler divergence
subject to the requirement that the expected return is
is the risk-free rate.