Abstract
Given a convex function $f$ and a set $\Q$ of probability measures, we consider the problem of minimizing the robust $f$-divergence $\infq f(P|Q)$ over the class $\PP$ of martingale measures. Under mild conditions on $\PP$ and $\Q$ we show that a minimizer exists within the class $\PP$ if $\lim_{x \rightarrow \infty} f(x)/x = \infty$. If $\lim_{x \rightarrow \infty} f(x)/x = 0$ then there is a minimizer in a class $\bar\PP$ of extended martingale measures defined on the predictable $\sigma$-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.
Citation
Hans Föllmer. Anne Gundel. "Robust projections in the class of martingale measures." Illinois J. Math. 50 (1-4) 439 - 472, 2006. https://doi.org/10.1215/ijm/1258059482
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