The relations between Minimal Martingale Measure and Minimal Entropy Martingale Measure

We consider incomplete markets, where each risky asset fluctuation is a continuous semimartingale, and study a subset of Equivalent Local Martingale Measures in which Minimal Martingale Measure minimizes relative entropy. We also discuss, as special cases, some models with the risky asset fluctuation represented as a solution of some stochastic differential equations. Finally, we mention that the predictable representation property is essential in order that Minimal Martingale Measure coincides with Minimal Entropy Martingale Measure.