Variance Minimization and Random Variables with Constant Sum

By Ludger Rüschendorf, Ludger Uckelmann. 2002

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An academic response to Basel II (2001, background): “Analytical values for VaRα(X d ) have been obtained in Wang et al. (2013) and Puccetti and Rüschendorf (2013) for the homogeneous model when the marginal distributions have a taildecreasing density (such as Pareto, Gamma or Lognormal distributions).”
An Academic Response to Basel 3.5 (2014, background): “In this case, the results reported in Section 3 tell us that the full VaR range [31, 465] is attainable (given that all marginal dfs are Pareto(2)); more research is needed concerning the question “which interdependencies (copulas) yield VaR values in the”
Model uncertainty and VaR aggregation (2013, background): “Some other examples of completely mixable distributions, as well as an insight into the theory of complete mixability, are given in Rüschendorf and Uckelmann (2002), Wang and Wang (2011) and Puccetti et al. (2012).”