Archimedean Utility Copulas with Polynomial Generating Functions

Abstract

Archimedean utility copulas comprise the general class of multiattribute utility functions that have additive ordinal preferences and are strictly increasing with each argument for at least one reference value of the complementary attributes. The construction of an Archimedean utility copula requires an assessment of an individual utility function for each attribute as well as a single generating function. The assessment of individual utility functions for the attributes of a decision has had a large share of literature coverage, but there has been much less literature on the construction of the generating function for the Archimedean functional form. This paper focuses on the assessment of Archimedean utility copulas with polynomial generating functions. We provide methods to assess these generating functions and derive bounds on the types of utility surfaces that they provide. We demonstrate that linear generating functions correspond to the multiplicative form of mutual utility independence, and then we show how higher-order polynomial generating functions allow more flexibility in the types of multiattribute utility functions and corner values that can be modeled. The results of this paper provide a new method to help the analyst construct multiattribute utility functions in a simple way when utility independence conditions do not hold.