Robust projections in the class of martingale measures

Given a convex function f and a set of probability measures, we consider the problem of minimizing the robust f-divergence f(P|Q) over the class of martingale measures. Under mild conditions on and we show that a minimizer exists within the class if limx → ∞ f(x)/x = ∞. If limx → ∞ f(x)/x = 0 then there is a minimizer in a class of extended martingale measures defined on the predictable σ-field. We also explain how both cases are connected to recent developments in the theory of optimal portfolio choice, in particular to robust extensions of the classical expected utility criterion.