Nonadditive Multiattribute Utility Functions for Portfolio Decision Analysis

Portfolio decision analysis models support selecting a portfolio of projects in view of multiple objectives and limited resources. In applications, portfolio utility is commonly modeled as the sum of the projects’ multiattribute utilities, although such approaches lack rigorous decision-theoretic justification. This paper establishes the axiomatic foundations of a more general class of multilinear portfolio utility functions, which includes additive and multiplicative portfolio utility functions as special cases. Furthermore, we develop preference elicitation techniques to assess these portfolio utility functions as well as optimization models to identify the most preferred portfolio in view of resource and other constraints. We also examine how the functional form of the portfolio utility function affects decision recommendations by using randomly generated and real problem instances.