A Composite Risk Measure Framework for Decision Making Under Uncertainty

  • Peng-Yu Qian
  • Zi-Zhuo Wang
  • Zai-Wen Wen


In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision if the exact distribution of uncertain model parameters were given, and the outer risk measure quantifies the risk that occurs when estimating the parameters of distribution. We show that the model is tractable under mild conditions. The framework is a generalization of several existing models, including stochastic programming, robust optimization, distributionally robust optimization. Using this framework, we study a few new models which imply probabilistic guarantees for solutions and yield less conservative results compared to traditional models. Numerical experiments are performed on portfolio selection problems to demonstrate the strength of our models.


Risk management Stochastic programming Portfolio management 

Mathematics Subject Classification



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Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of BusinessColumbia UniversityNew YorkUSA
  2. 2.Department of Industrial and Systems EngineeringUniversity of MinnesotaMinneapolisUSA
  3. 3.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina

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