Ordering higher risks in Yaari's dual theory

In Yaari's (1987) dual theory of choice under risk, risk preferences are based on a functional that incorporates a subjective distortion function. In the context of Wang's (1996) premium principle, Wang and Young (1998) introduce a sequence of partial ordering classes for risk distributions which characterize the preferences of groups of risk-averse agents making decisions based on this functional. Under this framework, if one distribution is perceived as less risky than another, its mean is smaller than or equal to the latter's, which can make certain risk distributions non-comparable. In this paper, we investigate a sequence of partial orders for risk distributions, grounded in comparisons of successive integrals of TVaR curves, that capture the preferences of agents primarily concerned with large risks that exceed their expected values. The normative properties of these orders are explored through the nth-degree coefficient of dual risk aversion, which serves as the dual analog of the index of absolute risk aversion introduced by Caballé and Pomansky (1996) within the expected utility model.