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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 ₗ f (x) /x =. If ₗ f (x) /x = 0 then there is a minimizer in a class of extended martingale measures defined on the predictable -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.
Föllmer et al. (Sun,) studied this question.
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