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BY 4.0 license Open Access Published by De Gruyter Open Access April 3, 2020

Checkerboard copula defined by sums of random variables

  • Viktor Kuzmenko , Romel Salam and Stan Uryasev EMAIL logo
From the journal Dependence Modeling

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.

MSC 2010: 62H05; 62H12; 90C25; 91-10

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Received: 2019-02-19
Accepted: 2020-03-02
Published Online: 2020-04-03

© 2020 Viktor Kuzmenko et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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