This paper considers a class of functions referred to as convex-concave-convex (CCC) functions to calibrate unimodal or multimodal probability distributions. In discrete case, this class of functions can be expressed by a system of linear constraints and incorporated into an optimization...

Systemic risk is the risk that the distress of one or more institutions trigger a collapse of the entire financial system. We extend CoVaR (value-at-risk conditioned on an institution) and CoCVaR (conditional value-at-risk conditioned on an institution) systemic risk contribution measures and...