Model-free bounds on Value-at-Risk using extreme value information and statistical distances

Thibaut Lux, Antonis Papapantoleon

We derive bounds on the distribution function, therefore also on the Value-at-Risk, of $\phi (\mathbf{X})$ where $\phi$ is an aggregation function and $\mathbf{X}=(X_1,\dots ,X_d)$ is a ra…