Convex analysis approach to utility theories. dual utility

We show that the dual (rank dependent) utility theory and the expected utility theory have common mathematical foundations. The main results of the dual utility theory can be derived from the separation principle of convex analysis and the integral representations of continuous linear functionals. This approach is similar to the one we have successfully applied to obtain the main results of the expected utility theory. Our results explain the dual character of utility functions. Additionally, we provide two new representations of dual utility.