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XII Symposium of Probability and Stochastic ProcessesCharacterization of the Minimal Penalty of a Convex Risk Measure with Applications to Robust Utility Maximization for Lévy Models

XII Symposium of Probability and Stochastic Processes: Characterization of the Minimal Penalty of... [The minimality of the penalty function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and closed subset of the absolutely continuous measures with respect to some reference measure ℙ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {P}$$ \end{document} to be minimal on this set. When the probability space supports a Lévy process, we establish results that guarantee the minimality property of a penalty function described in terms of the coefficients associated with the density processes. These results are applied in the solution of the robust utility maximization problem for a market model based on Lévy processes.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

XII Symposium of Probability and Stochastic ProcessesCharacterization of the Minimal Penalty of a Convex Risk Measure with Applications to Robust Utility Maximization for Lévy Models

Part of the Progress in Probability Book Series (volume 73)
Editors: Hernández-Hernández, Daniel; Pardo, Juan Carlos; Rivero, Victor
Hernández-Hernández, Daniel; Pérez-Hernández, Leonel
XII Symposium of Probability and Stochastic Processes — Jun 27, 2018
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References (12)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing AG, part of Springer Nature 2018
ISBN
978-3-319-77642-2
Pages
135 –168
DOI
10.1007/978-3-319-77643-9_4
Publisher site
See Chapter on Publisher Site

Abstract

[The minimality of the penalty function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and closed subset of the absolutely continuous measures with respect to some reference measure ℙ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {P}$$ \end{document} to be minimal on this set. When the probability space supports a Lévy process, we establish results that guarantee the minimality property of a penalty function described in terms of the coefficients associated with the density processes. These results are applied in the solution of the robust utility maximization problem for a market model based on Lévy processes.]

Published: Jun 27, 2018

Keywords: Convex risk measures; Fenchel-Legendre transformation; Minimal penalization; Lévy process; Robust utility maximization; 91B30; 46E30

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