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 scala...

We study issues of robustness in the context Quantitative Risk Management and Optimization. develop a general methodology for determining whether given risk-measurement-related optimization problem is robust, which we call “robustness against optimization.” The new notion studied various classes risk measures expected utility loss functions. Motivated by practical from !nancial regulation, spec...

The Expected Shortfall (ES) is one of the most important regulatory risk measures in finance, insurance, and statistics, which has recently been characterized via sets axioms from perspectives portfolio management statistics. Meanwhile, there large literature on insurance design with ES as an objective or a constraint. A visible gap to justify special role actuarial science. To fill this gap, w...