Choquet rating criteria, risk measures, and risk consistency

Abstract: Credit ratings are widely used by investors as a screening device. We introduce and study several natural notions of risk consistency that promote prudent investment decisions in the framework of Choquet rating criteria. Three closely related notions of risk consistency are considered: with respect to risk aversion, the asset pooling effect, and the benefit of portfolio diversification. These notions are formulated either under a single probability measure or multiple probability measures. We show how these properties translate between rating criteria and the corresponding risk measures, and establish a hierarchical structure among them. These findings lead to a full characterization of Choquet risk measures and Choquet rating criteria satisfying risk consistency properties. Illustrated by case studies on collateralized loan obligations and catastrophe bonds, some classes of Choquet rating criteria serve as useful alternatives to the probability of default and expected loss criteria used in practice for rating financial products.