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Martingale characterizations of risk-averse stochastic optimization problems

  • Alois PichlerEmail author
  • Ruben Schlotter
Full Length Paper Series B
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Abstract

This paper addresses risk awareness of stochastic optimization problems. Nested risk measures appear naturally in this context, as they allow beneficial reformulations for algorithmic treatments. The reformulations presented extend usual dynamic equations by involving risk awareness in the problem formulation. Nested risk measures are built on risk measures, which originate by conditioning on the history of a stochastic process. We derive martingale properties of these risk measures and use them to prove continuity. It is demonstrated that stochastic optimization problems, which incorporate risk awareness via nesting risk measures, are continuous with respect to the natural distance governing these optimization problems, the nested distance.

Keywords

Risk measures Stochastic optimization Stochastic processes 

Mathematics Subject Classification

90C15 60B05 62P05 

Notes

Acknowledgements

We would like to thank Prof. Shapiro for proposing to elaborate the continuity relations of nested risk measures with respect to the nested distance.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019

Authors and Affiliations

  1. 1.Technische Universität ChemnitzChemnitzGermany

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