Optimization models for cumulative prospect theory under incomplete preference information

Prospect stochastic dominance conditions can be used to compare pairs of uncertain decision alternatives when the decision makers’ choice behavior is characterized by cumulative prospect theory, but their preferences are not precisely specified. This paper extends the use of prospect stochastic dominance conditions to decision settings in which the use of pairwise comparisons is not possible due to large or possibly infinite number of decision alternatives (e.g., financial portfolio optimization). In particular, we first establish equivalence results between these conditions and the existence of solutions to a specific system of linear inequalities. We then utilize these results to develop stochastic optimization models whose feasible solutions are guaranteed to dominate a pre-specified benchmark distribution. These models can be used to identify if there exists a decision alternative within a set that is preferred to a given benchmark by all decision makers with an S-shaped value function and a pair of inverse S-shaped probability weighting functions. Thus, the models offer a flexible tool to analyze choice behavior in decision settings that can be modeled as optimization problems. We demonstrate the use of the developed models with two empirical applications in financial portfolio diversification and procurement optimization.