Ricerc@Sapienza

We study preference relations on conditional gambles of a decision maker acting under ambiguity. Dutch book rationality conditions are provided under a linear utility scale, encoding either an optimistic or a pessimistic attitude towards uncertainty. These conditions characterize possibly incomplete preferences representable by totally alternating or monotone conditional functionals. In general, the uniqueness of the representation is not guaranteed, but it can be obtained by adding the hypothesis of existence of a conditional fair price for every conditional gamble.

Investors often need to look for an optimal portfolio acting under ambiguity, as they may not be able to single out a unique realworld probability measure. In this paper a discrete-time dynamic portfolio selection problem is studied, referring to an -contaminated binomial market model and assuming investors’ preferences are consistent with the Choquet expected utility theory.

We manage decisions under “objective” ambiguity by considering generalized Anscombe-Aumann acts, mapping states of the world to generalized lotteries on a set of consequences. A generalized lottery is modeled through a belief function on consequences, interpreted as a partially specified randomizing device. Preference relations on these acts are given by a decision maker focusing on different scenarios (conditioning events).