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