Many asset pricing theories treat the cross-section of returns volatility and correlations as two intimately related quantities driven by common factors, which hinders achieving a neat definition of a correlation premium. We formulate a model without factors, but with a continuum of securities...

We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding adjusted Expected Shortfalls quantify risk as the minimum...