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Checkerboard copula defined by sums of random variables

Author

Listed:
  • Kuzmenko Viktor

    (V.M.Glushkov Institute of Cybernetics,Kyiv, Ukraine)

  • Salam Romel

    (Fellow of the Casualty Actuarial Society and Member of the American Academy of Actuaries)

  • Uryasev Stan

    (Applied Mathematics and Statistics, Stony Brook University, USA)

Abstract

We consider the problem of finding checkerboard copulas for modeling multivariate distributions. A checkerboard copula is a distribution with a corresponding density defined almost everywhere by a step function on an m-uniform subdivision of the unit hyper-cube. We develop optimization procedures for finding copulas defined by multiply-stochastic matrices matching available information. Two types of information are used for building copulas: 1) Spearman Rho rank correlation coefficients; 2) Empirical distributions of sums of random variables combined with empirical marginal probability distributions. To construct checkerboard copulas we solved optimization problems. The first problem maximizes entropy with constraints on Spearman Rho coefficients. The second problem minimizes some error function to match available data. We conducted a case study illustrating the application of the developed methodology using property and casualty insurance data. The optimization problems were numerically solved with the AORDA Portfolio Safeguard (PSG) package, which has precoded entropy and error functions. Case study data, codes, and results are posted at the web.

Suggested Citation

  • Kuzmenko Viktor & Salam Romel & Uryasev Stan, 2020. "Checkerboard copula defined by sums of random variables," Dependence Modeling, De Gruyter, vol. 8(1), pages 70-92, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:70-92:n:4
    DOI: 10.1515/demo-2020-0004
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    References listed on IDEAS

    as
    1. Mafusalov, Alexander & Uryasev, Stan, 2016. "CVaR (superquantile) norm: Stochastic case," European Journal of Operational Research, Elsevier, vol. 249(1), pages 200-208.
    2. Pfeifer Dietmar & Tsatedem Hervé Awoumlac & Mändle Andreas & Girschig Côme, 2016. "New copulas based on general partitions-of-unity and their applications to risk management," Dependence Modeling, De Gruyter, vol. 4(1), pages 123-140, July.
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