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, ${\displaystyle P}$, and the risk-neutral measure, ${\displaystyle Q}$. 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 ${\displaystyle Q}$ will always be equivalent to the measure ${\displaystyle P}$ 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 ${\displaystyle Q}$ will not be equivalent to ${\displaystyle P}$.

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