This was part of Decision Making and Uncertainty

Choquet quantiles

Ruodu Wang, University of Waterloo

Wednesday, February 7, 2024


Choquet capacities and integrals are useful concepts for modeling decision under uncertainty, pioneered by Schmeidler. We study a class of functionals, called Choquet quantiles, which are Choquet integrals with respect to binary capacities. Choquet quantiles are a generalization of probabilistic quantiles, also known as Value-at-Risk in finance. Choquet quantiles enjoy many nice properties of probabilistic quantiles, in the contexts of axiomatic representation, optimization formulas, and risk sharing. In particular, Choquet quantiles are characterized by only one axiom, called ordinality, and the inf-convolution of Choquet quantiles is again a Choquet quantile. Moreover, we introduce the Choquet Expected Shortfall, giving rise to a new class of coherent risk measures under uncertainty.