M. Mania, R. Tevzadze
We give a unified characterization of $q$-optimal martingale measures for $q\in [0,\infty)$ in an incomplete market model, where the dynamics of asset prices are described by a continuous
semimartingale. According to this characterization the variance-optimal, the minimal entropy and the minimal martingale measures appear as the special cases $q=2$, $q=1$ and $q=0$ respectively. Under assumption that the Reverse Hölder condition is satisfied, the continuity (in $L^1$ and in entropy) of
densities of $q$-optimal martingale measures with respect to $q$ is proved.