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CVaR distance between univariate probability distributions and approximation problems

Author

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  • Konstantin Pavlikov

    (University of Southern Denmark)

  • Stan Uryasev

    (University of Florida)

Abstract

The paper defines new distances between univariate probability distributions, based on the concept of the CVaR norm. We consider the problem of approximation of a discrete distribution by some other discrete distribution. The approximating distribution has a smaller number of atoms than the original one. Such problems, for instance, must be solved for generation of scenarios in stochastic programming. The quality of the approximation is evaluated with new distances suggested in this paper. We use CVaR constraints to assure that the approximating distribution has tail characteristics similar to the target distribution. The numerical algorithm is based on two main steps: (i) optimal placement of positions of atoms of the approximating distribution with fixed probabilities; (ii) optimization of probabilities with fixed positions of atoms. These two steps are iterated to find both optimal atom positions and probabilities. Numerical experiments show high efficiency of the proposed algorithms, solved with convex and linear programming.

Suggested Citation

  • Konstantin Pavlikov & Stan Uryasev, 2018. "CVaR distance between univariate probability distributions and approximation problems," Annals of Operations Research, Springer, vol. 262(1), pages 67-88, March.
    • Handle: RePEc:spr:annopr:v:262:y:2018:i:1:d:10.1007_s10479-017-2732-8
    DOI: 10.1007/s10479-017-2732-8
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    References listed on IDEAS

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    Cited by:

    1. Pertaia Giorgi & Uryasev Stan, 2019. "Fitting heavy-tailed mixture models with CVaR constraints," Dependence Modeling, De Gruyter, vol. 7(1), pages 365-374, January.
    2. Juan Li & Bin Xin & Panos M. Pardalos & Jie Chen, 2021. "Solving bi-objective uncertain stochastic resource allocation problems by the CVaR-based risk measure and decomposition-based multi-objective evolutionary algorithms," Annals of Operations Research, Springer, vol. 296(1), pages 639-666, January.
    3. Alessandro Barbiero & Asmerilda Hitaj, 2023. "Discrete approximations of continuous probability distributions obtained by minimizing Cramér-von Mises-type distances," Statistical Papers, Springer, vol. 64(5), pages 1669-1697, October.

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