**M. Mania, R. Tevzadze**

## A Unified Characterization of *q*-optimal
and Minimal Entropy Martingale Measures by Semimartingale Backward Equations

**abstract:**

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.