VaR bounds for joint portfolios with dependence constraints

Based on a novel extension of classical Hoe ding-Fréchet bounds, we provide an upper VaR bound for joint risk portfolios with xed 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 con dence level and its quality is illustrated in a series of examples of practical interest.