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For incomplete preference relations that are represented by multiple priorsand/or multiple -- possibly multivariate -- utility functions, we define acertainty equivalent as well as the utility buy and sell prices andindifference price bounds as set-valued functions of the claim. Furthermore, wemotivate and introduce the notion of a weak and a strong certainty equivalent.We will show that our definitions contain as special cases some definitionsfound in the literature so far on complete or special incomplete preferences.We prove monotonicity and convexity properties of utility buy and sell pricesthat hold in total analogy to the properties of the scalar indifference pricesfor complete preferences. We show how the (weak and strong) set-valuedcertainty equivalent as well as the indifference price bounds can be computedor approximated by solving convex vector optimization problems. Numericalexamples and their economic interpretations are given for the univariate aswell as for the multivariate case.

Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization