VaR bounds for joint portfolios with dependence constraints

Giovanni Puccetti 1 , Ludger Rüschendorf 2 , and Dennis Manko 2
  • 1 Department of Economics, Management and Quantitative Methods, University of Milano, Italy
  • 2 Department of Mathematical Stochastics, University of Freiburg, Germany


Based on a novel extension of classical Hoeffding-Fréchet bounds, we provide an upper VaR bound for joint risk portfolios with fixed marginal distributions and positive dependence information. The positive dependence information can be assumed to hold in the tails, in some central part, or on a general subset of the domain of the distribution function of a risk portfolio. The newly provided VaR bound can be interpreted as a comonotonic VaR computed at a distorted confidence level and its quality is illustrated in a series of examples of practical interest.

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