Minimal-entropy martingale measure
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, formula_1, and the risk-neutral measure, formula_2. 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 formula_2 will always be equivalent to the measure formula_1 by construction. 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 formula_2 will not be equivalent to formula_1. In a finite probability model, for objective probabilities formula_7 and risk-neutral probabilities formula_8 then one must minimise the Kullback–Leibler divergence formula_9 subject to the requirement that the expected return is formula_10, where formula_10 is the risk-free rate.