Choquet integrals and capacities play a crucial role in modern decision theory. Comonotony is a central concept for these theories because the main property of a Choquet integral is its additivity for comonotone functions. We consider a Choquet integral representation of preferences showing uncertainty aversion (pessimism) and propose axioms on time consistency which yield a candidate for conditional Choquet integrals. An other axiom characterizes the role of comonotony in the use of information. We obtain two conditioning rules for capacities which (...) amount to the well-known Bayes' and Dempster–Schafer's updating rules. We are allowed to interpret both of them as a lack of confidence in information in a dynamic extension of pessimism. (shrink)

We study the Full Bayesian Updating rule for convex capacities. Following a route suggested by Jaffray (IEEE Transactions on Systems, Man and Cybernetics 22(5):1144–1152, 1992), we define some properties one may want to impose on the updating process, and identify the classes of (convex and strictly positive) capacities that satisfy these properties for the Full Bayesian Updating rule. This allows us to characterize two parametric families of convex capacities: ${(\varepsilon,\delta)}$ -contaminations (which were introduced, in a slightly different form, by Huber (...) (Robust Statistics, Wiley, New York, 1981)) and ${\varepsilon}$ -contaminations. (shrink)

A usual argument in finance refers to no arbitrage opportunities for the positivity of the bid-ask spread. Here we follow the decision theory approach and show that if positivity of the bid-ask spread is identified with strong risk aversion for an expected utility market-maker, this is no longer true for a rank-dependent expected utility one. For such a decision-maker only a very weak form of risk aversion is required, a result which seems more in accordance with his actual behavior. We (...) conclude by showing that the no-trade interval result of Dow and Werlang (1992a) remains valid for a rank-dependent expected utility market-maker merely exhibiting this weak form of risk aversion. (shrink)

This paper considers a decision-making process under ambiguity in which the decision-maker is supposed to split outcomes between familiar and unfamiliar ones. She is assumed to behave differently with respect to unfamiliar gains, unfamiliar losses and customary (familiar) outcomes. In particular, she is supposed to be pessimistic on gains, optimistic on losses and ambiguity neutral on the familiar outcomes. A generalization of the usual Choquet Integral is formalized when the decision maker holds capacities and probabilities. A characterization of the decision-maker’s (...) behavior is provided for a specific subset of capacities, in which it is shown that the decision-maker underestimates the unfamiliar outcomes while is linear in probabilities on customary ones. (shrink)

We axiomatize, in the multidimensional case, a social evaluation function that can accommodate a natural Pigou–Dalton principle and correlation increasing majorization. This is performed by building upon a simple class of inframodular functions proposed by Müller and Scarsini under risk.

The main purpose of this paper is to show that left-monotone risk aversion, a meaningful refinement of strong risk aversion, characterizes decision makers for whom deductible insurance is optimal. A second goal is to prove that the deductible’s computation is particularly tractable in the case of Yaari’s decision makers.

Tribute to Jean-Yves Jaffray by the French Group of Decision Theory.

We argue, in the spirit of some of Jean-Yves Jaffray’s work, that explicitly incorporating the information, however imprecise, available to the decision maker is relevant, feasible, and fruitful. In particular, we show that it can lead us to know whether the decision maker has wrong beliefs and whether it matters or not, that it makes it possible to better model and analyze how the decision maker takes into account new information, even when this information is not an event and finally (...) that it is crucial when attempting to identify and measure the decision maker’s attitude toward imprecise information. (shrink)