Characterization of the Minimal Penalty of a Convex Risk Measure with Applications to Robust Utility Maximization for Lévy Models

  • Daniel Hernández-Hernández
  • Leonel Pérez-Hernández
Conference paper
Part of the Progress in Probability book series (PRPR, volume 73)


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.


Convex risk measures Fenchel-Legendre transformation Minimal penalization Lévy process Robust utility maximization 

Mathematics Subject Classification

91B30 46E30 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Daniel Hernández-Hernández
    • 1
  • Leonel Pérez-Hernández
    • 2
  1. 1.Centro de Investigación en MatemáticasGuanajuatoMexico
  2. 2.Departamento de Economía y FinanzasUniversidad de GuanajuatoGuanajuatoMexico

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