Research

Inspired by the results of Ambiguity, Randomization and the Timing of Resolution of Uncertainty this project aims to develop a purely behavioral approach to the beliefs functions based on a comparative notion of comonotonicity.  

Intuitively, the aforementioned article demonstrates that, within the ECU model, certain properties of a capacity—such as the non-emptiness of its core, convexity, and additivity—can be characterized in terms of a preference for “comonotonicity” when comparing different sets of acts. However, some properties remain unaddressed, most notably that of Total Monotonicity, which is stronger than convexity but weaker than additivity. Despite its central role in the theory of belief functions, the latter has received little axiomatic justification so far, raising the natural question of whether our study can be extended to this case. Preliminary results suggest that, in our framework, the capacity corresponds to a belief function if and only if the decision-maker exhibits a preference  for “greater comonotonicity,” in a sense that remains to be rigorously defined. 

The paper Discounted Subjective Expected Utility in Continuous Time written by Bastianello and Vergopoulos provides a joint axiomatic characterization of both Exponential Discounting and Subjective Expected Utility, accommodating arbitrary state and outcome spaces. To establish their representation, the authors build on the Anscombe-Aumann theorem and the Independence axiom, which they derive from their own axiom of Stationarity. 

As demonstrated by Schmeidler (1989), restricting the Independence axiom to comonotonic functions leads to a more general representation that allows for non-additive probabilities and thus to account for ambiguity aversion. However, this natural weakening does not directly extend to Stationarity, preventing the DSEU model from incorporating ambiguity aversion. In this paper, we propose an alternative axiomatic framework that accommodates the desired weakening, thereby yielding an extended representation in which the decision-maker’s beliefs are represented by a capacity.

In 2017, Bommier published an article entitled A dual approach to ambiguity aversion whose central idea closely relates to the one developed in Ambiguity, Randomization and the Timing of Resolution of Uncertainty. 

Yet, the two models yield distinct predictions. In this paper, we undertake a systematic analysis of the differences between what we shall refer to as “dual models”. In particular, we demonstrate that certain models display a higher degree of ambiguity aversion in the sense of Marinacci and Ghirardato (2002) but also with respect to the No-Trade Intervals of Dow and Werlang (1992). 

The classic framework of Anscombe and Aumann for decision-making under uncertainty postulates both a primary source of uncertainty (the “horse race”) and an auxiliary randomization device (the “roulette wheel”). It also imposes a specific timing of resolution of uncertainty as the horse race takes place before the roulette is played. 

While this timing is without loss of generality for Subjective Expected Utility, it forbids plausible choice patterns of ambiguity aversion. In this paper, we reverse this timing by assuming that the roulette is played prior to the horse race and we obtain an axiomatic characterization of Choquet Expected Utility that is dual to that of Schmeidler (1989). In this representation, ambiguity aversion is characterized by an aversion to conditioning roulette acts on horse events which, as we argue, is more plausible. Moreover, it can be larger than in Schmeidler’s model. Finally, our reversed timing yields incentive compatibility of the random incentive mechanisms, frequently used in experiments for eliciting ambiguity attitudes.

This paper studies decision-making in the face of two stochastically independent sources of uncertainty. It characterizes axiomatically a Subjective Expected Utility representation of preferences where subjective beliefs consist of a product probability measure. The two key axioms in this characterization both involve some behavioral notions of stochastic independence. Our result can be understood as a purely subjective version of the Anscombe and Aumann  (1963) theorem that avoids the controversial use of exogenous probabilities by appealing to stochastic independence. We also obtain an extension to Choquet Expected Utility representations.

This paper studies decision-making under uncertainty and introduces a new preference axiom called Subjective Independence. The latter requires some consistency between two forms of stochastic independence that can be inferred from choice behavior. Yet it can also be understood as a purely subjective version of the classical Independence axiom commonly used under risk. The main result presented in this paper uncovers the role that Subjective Independence plays in the axiomatic characterization of Subjective Expected Utility preferences.