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2006 Robust projections in the class of martingale measures
Hans Föllmer, Anne Gundel
Illinois J. Math. 50(1-4): 439-472 (2006). DOI: 10.1215/ijm/1258059482

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

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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

Information

Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1099.94016
MathSciNet: MR2247836
Digital Object Identifier: 10.1215/ijm/1258059482

Subjects:
Primary: 60G44
Secondary: 49N15, 60G48, 91B16, 91B28, 94A17

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign

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Vol.50 • No. 1-4 • 2006
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