Coherent Moment-Based Approximations of Risk Functionals

The paper introduces a new, moment-based representation of version independent, coherent risk functionals for distributions with a finite second moment. The representation is based on L-moments. We analyze the second- and the third-order approximations and provide a method for constructing coherent approximations with the first few moments of the distribution. The method can be applied to coherent and non-coherent risk functionals and is interpreted in terms of a weighted average of particular Bayesian versions of Conditional Value-at-Risk. We formulate a conservative risk functional and a minimax portfolio construction problem which is non-parametric, convex, and exhibits a relative statistical robustness of the optimal solution compared to the classical utility-based approach. The developed approach bridges the gap between the intuitive utility-based higher-order moment portfolio construction and the formal construct of coherent risk functionals.