Mono-Linearity-Based Axiomatic Approach to Non-Linear Expected Utility

In this paper, we study the theory of preference over unbounded random prospects using an axiomatic approach. We first show that Yaari's dual independence axiom can be decomposed into two axioms, the homogeneity axiom and the co-monotonic independence with respect to addition axiom, and we determine the representational form using the first axiom and the two axioms jointly. We then show that the second axiom is equivalent to a mono-linearity axiom, which characterizes a local linearity property of preference. Our work provides an axiomatic approach to the smooth preference model developed by Machina and Chew et al.; this paper may thus be regarded as a bridge between the dual theory of Yaari and the smooth preference model of Machina and Chew et al., and it extends their results to unbounded outcome spaces. Homogeneity and mono-linearity provide additional flexibility in characterizing irregular behavior, and examples are provided to illustrate their applications