This work presents a framework for constructing elicitable risk measures with properties like monotonicity, translation invariance, and convexity using multiplicative scoring functions. It defines necessary conditions for these properties and provides a method for developing new elicitable functionals, with applications in finance, statistics, and machine learning.
"Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures."
"This paper introduces and fully characterizes the novel class of quasi-logconvex measures of risk, to stand on equal footing with the rich class of quasi-convex measures of risk."
"We extend the scope of risk measures for which backtesting models are available by proposing a multinomial backtesting method for general distortion risk measures. The method relies on a stratification and randomization of risk levels. We illustrate the performance of our methods in numerical case studies."
"... results are applied in a wide range of actuarial problems including multivariate risk measures, aggregate loss, large claims reinsurance, weighted premium calculations and risk capital allocation. "