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.
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Hernández-Hernández, D., Pérez-Hernández, L. (2018). Characterization of the Minimal Penalty of a Convex Risk Measure with Applications to Robust Utility Maximization for Lévy Models. In: Hernández-Hernández, D., Pardo, J., Rivero, V. (eds) XII Symposium of Probability and Stochastic Processes. Progress in Probability, vol 73. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-77643-9_4
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DOI: https://doi.org/10.1007/978-3-319-77643-9_4
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