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.
@article{1258059482,
author = {F\"ollmer, Hans and Gundel, Anne},
title = {Robust projections in the class of martingale measures},
journal = {Illinois J. Math.},
volume = {50},
number = {1-4},
year = {2006},
pages = { 439-472},
language = {en},
url = {http://dml.mathdoc.fr/item/1258059482}
}
Föllmer, Hans; Gundel, Anne. Robust projections in the class of martingale measures. Illinois J. Math., Tome 50 (2006) no. 1-4, pp. 439-472. http://gdmltest.u-ga.fr/item/1258059482/