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Scaling Limits of Markov-Branching Trees and Applications Read chapter Read first chapter

2018 | OriginalPaper | Chapter

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

Authors : Daniel Hernández-Hernández, Leonel Pérez-Hernández

Published in: XII Symposium of Probability and Stochastic Processes

Publisher: Springer International Publishing

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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.

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previous chapter Asymptotic Results for the Severity and Surplus Before Ruin for a Class of Lévy Insurance Processes
next chapter Blackwell-Nash Equilibria in Zero-Sum Stochastic Differential Games
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Metadata
Title
Characterization of the Minimal Penalty of a Convex Risk Measure with Applications to Robust Utility Maximization for Lévy Models
Authors
Daniel Hernández-Hernández
Leonel Pérez-Hernández
Copyright Year
2018
Book
XII Symposium of Probability and Stochastic Processes

Print ISBN: 978-3-319-77642-2

Electronic ISBN: 978-3-319-77643-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-77643-9_4