In this paper, we derive upper and lower bounds on the Range Value-at-Risk of the portfolio loss when we only know its mean and variance, and its feature of unimodality. In a first step, we use some classic results on stochastic ordering to reduce this optimization problem to a parametric one,...

We derive upper and lower bounds for the Range Value-at-Risk of a unimodal random variable under knowledge of the mean, variance, symmetry, and a possibly bounded support. Moreover, we provide a generalization of the Gauss inequality for symmetric distributions with known support