Comparing the minimal Hellinger martingale measure of order $q$ to the $q$-optimal martingale measure
Résumé
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 1. First, we provide more results for the MHM measure; in particular we establish its complete characterization in two manners. Then we derive two equivalent conditions for both martingale measures to coincide. These conditions are in particular fulfilled in the case of markets driven by Levy processes. Finally, we analyze the MHM measure as well as its relationship to the q-optimal martingale measure for the case of a discrete-time market model