Robust projections in the class of martingale measures

Abstract

Given a convex function f and a set Q of probability measures, we consider the problem of minimizing the robust f-divergence infQ∈Q f(P|Q) over the class P of martingale measures. Under mild conditions on P and Q we show that a minimizer exists within the class P if limx→∞ f(x)/x = ∞. If limx→∞Kx, f(x)/x = 0 then there is a minimizer in a class P 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. © 2006 University of Illinois.