Representation of subjective preferences under ambiguity

The objective of this paper is to show how potentially incomplete preferences of a decision maker (DM) on acts can be modelled formally in a subjective ambiguity perspective We identify acts as functions from a state space Omega to bounded support (finitely additive) probabilities over a set X of prizes. Then, we characterize preferences over equibounded acts a which have a numerical representation by the family of functionals {J(pi)(a) = integral(Omega) [integral(X) u(x)a(omega)(dx)]pi(d omega); pi epsilon Pi}, where u is a cardinal utility on X (representing the risk attitude of the DM) and Pi is a unique pointwise closed convex set of probabilities on all events in Omega (representing the ambiguity perceived by the DM). To this end, in addition to the usual independence and continuity assumptions, we add completeness and dominance for preferences restricted to constant acts; moreover, we consider two other properties (subjective monotonicity and coherence) related with the preferences of a DM who is not able, owing to his partial knowledge, to evaluate any event in Omega. (c) 2005 Elsevier Inc. All rights reserved.