This paper presents a new axiomatic characterization of risk measures that are additive for independent random variables. In contrast to previous work, we include an axiom that guarantees monotonicity of the risk measure. Furthermore, the axiom of additivity for independent random variables is...

We compare seven established risk elicitation methods and investigate how they robustly explain eleven kinds of risky behavior with 760 individuals. Risk measures are positively correlated; however, their performance in explaining behavior is heterogeneous and, therefore, difficult to assess ex...

Many practitioners annualize VaR just like the standard deviation. We show that this approach is incorrect, and a more sophisticated formula should be used for deriving a periodic VaR from parameters of the daily returns distribution. Another problem addressed here is the distribution of daily...

Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a number of risk measures that are of the form of ratios,...

Using equations that arise in quantum mechanics, this paper describes a way to more accurately and efficiently represent non-Gaussian return distributions than the standard method of invoking skewness and kurtosis. Then, it provides a new single intuitive number, defined here as the “crash...

We introduce a family of Capital allocation rules (C.A.R) based on the dual representation for risk measures and inspired to the Aumann-Shapley allocation principle. These rules extend the one of Denault and Kalkbrener (for coherent risk measures) and the one of Tsanakas (convex case), to the...