On conditional Chisini means and risk measures

Given a real valued functional T on the space of bounded random variables, we investigate problem existence conditional version nonlinear means. We follow seminal idea by Chisini (1929), defining mean as solution equation induced T. provide sufficient conditions which guarantee (unique) system infinitely many equations, will so-called Conditional mean. apply our findings in characterizing scalarization Risk Measures, an essential tool originally adopted Detlefsen and Scandolo (2005) to deduce robust dual representation.