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Statistical estimation of composite risk functionals and risk optimization problems

Author

Listed:
  • Darinka Dentcheva

    (Stevens Institute of Technology)

  • Spiridon Penev

    (The University of New South Wales)

  • Andrzej Ruszczyński

    (Rutgers University)

Abstract

We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance, insurance, and other areas associated with optimization under uncertainty and risk. We establish central limit theorems for composite risk functionals. Furthermore, we discuss the asymptotic behavior of optimization problems whose objectives are composite risk functionals and we establish a central limit formula of their optimal values when an estimator of the risk functional is used. While the mathematical structures accommodate commonly used coherent measures of risk, they have more general character, which may be of independent interest.

Suggested Citation

  • Darinka Dentcheva & Spiridon Penev & Andrzej Ruszczyński, 2017. "Statistical estimation of composite risk functionals and risk optimization problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 737-760, August.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:4:d:10.1007_s10463-016-0559-8
    DOI: 10.1007/s10463-016-0559-8
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    References listed on IDEAS

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    Cited by:

    1. Tomasz Kosmala & Randall Martyr & John Moriarty, 2020. "Markov risk mappings and risk-sensitive optimal prediction," Papers 2001.06895, arXiv.org, revised Sep 2022.
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    3. Yin Liu & Sam Davanloo Tajbakhsh, 2023. "Stochastic Composition Optimization of Functions Without Lipschitz Continuous Gradient," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 239-289, July.
    4. Mert Gürbüzbalaban & Andrzej Ruszczyński & Landi Zhu, 2022. "A Stochastic Subgradient Method for Distributionally Robust Non-convex and Non-smooth Learning," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1014-1041, September.

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