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A Composite Risk Measure Framework for Decision Making Under Uncertainty

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Abstract

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.

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Notes

  1. A \(\phi \)-divergence is a functional that measures the distance between two probability distributions. Such functionals include the Kullback–Leibler divergence, the chi-squared divergence.

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Authors and Affiliations

  1. Graduate School of Business, Columbia University, New York, NY, 10027, USA

    Peng-Yu Qian

  2. Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Zi-Zhuo Wang

  3. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China

    Zai-Wen Wen

Authors
  1. Peng-Yu Qian
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  2. Zi-Zhuo Wang
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  3. Zai-Wen Wen
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Correspondence to Peng-Yu Qian.

Additional information

This paper is dedicated to Professor Yin-Yu Ye in celebration of his 70th birthday.

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Qian, PY., Wang, ZZ. & Wen, ZW. A Composite Risk Measure Framework for Decision Making Under Uncertainty. J. Oper. Res. Soc. China 7, 43–68 (2019). https://doi.org/10.1007/s40305-018-0211-9

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  • DOI: https://doi.org/10.1007/s40305-018-0211-9

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