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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Characterization of the Minimal Penalty of a Convex Risk Measure with Applications to Robust Utility Maximization for Lévy Models
verfasst von : Daniel Hernández-Hernández, Leonel Pérez-Hernández
Erschienen in: XII Symposium of Probability and Stochastic Processes
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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 \(\mathbb {P}\) 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.