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Conditioning Capacities and Choquet Integrals: The Role of Comonotony

Alain Chateauneuf, Robert Kast & André Lapied

Theory and Decision 51 (2/4):367-386 (2001)

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Asymmetric Choquet random walks and ambiguity aversion or seeking.Rossella Agliardi - 2017 - Theory and Decision 83 (4):591-602.details Asymmetric Choquet random walks are defined, in the form of dynamically consistent random walks allowing for asymmetric conditional capacities. By revisiting Kast and Lapied and Kast et al. we show that some findings regarding the effects of ambiguity aversion are preserved in the more general framework, which is of interest in several applications to policy making, risk management, corporate decisions, real option valuation of investment/ disinvestment projects, etc. The effect of ambiguity on the higher moments is investigated, as well, as (...) Download Export citation Bookmark
Valuing future cash flows with non separable discount factors and non additive subjective measures: conditional Choquet capacities on time and on uncertainty. [REVIEW]Robert Kast & André Lapied - 2010 - Theory and Decision 69 (1):27-53.details We consider future cash flows that are contingent both on dates in time and on uncertain states. The decision maker (DM) values the cash flows according to its decision criterion: Here, the payoffs’ expectation with respect to a capacity measure. The subjective measure grasps the DM’s behaviour in front of the future, in the spirit of de Finetti’s (1930) and of Yaari’s (1987) Dual Theory in the case of risk. Decomposition of the criterion into two criteria that represent the DM’s (...) Download Export citation Bookmark 1 citation
A note on “Re-examining the law of iterated expectations for Choquet decision makers”.André Lapied & Pascal Toquebeuf - 2013 - Theory and Decision 74 (3):439-445.details This note completes the main result of Zimper, by showing that additional conditions are needed in order the law of iterated expectations to hold true for Choquet decision makers. Due to the comonotonic additivity of Choquet expectations, the equation E[f, ν] = E[E[f, ν], ν], is valid only when the act f is comonotonic with its dynamic form, that we name “conditional certainty equivalent act”. Download Export citation Bookmark 1 citation
A representation of preferences by the Choquet integral with respect to a 2-additive capacity.Brice Mayag, Michel Grabisch & Christophe Labreuche - 2011 - Theory and Decision 71 (3):297-324.details In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI. Download Export citation Bookmark
Representability of Ordinal Relations on a Set of Conditional Events.Giulianella Coletti & Barbara Vantaggi - 2006 - Theory and Decision 60 (2-3):137-174.details Any dynamic decision model should be based on conditional objects and must refer to (not necessarily structured) domains containing only the elements and the information of interest. We characterize binary relations, defined on an arbitrary set of conditional events, which are representable by a coherent generalized decomposable conditional measure and we study, in particular, the case of binary relations representable by a coherent conditional probability. Download Export citation Bookmark 1 citation

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