This paper investigates the relationship between the minimal Hellinger martingale measure of order q (MHM measure hereafter) and the q-optimal martingale measure for any q[not equal to]1. First, we provide more results for the MHM measure; in particular we establish its complete characterization...

We provide a rate for the strong convergence of Euler approximations for stochastic differential equations (SDEs) whose diffusion coefficient is not Lipschitz but only (1/2+[alpha])-Hölder continuous for some [alpha]>=0.