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,...

In this paper, we propose a new non-parametric density estimator derived from the theory of frames and Riesz bases. In particular, we propose the so-called bi-orthogonal density estimator based on the class of B-splines, and derive its theoretical properties including the asymptotically optimal...