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This note completes the main result of Zimper (Theory and decision, doi:10.1007/s11238-010-9221-8, 2010), 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(dω)] = E[E[f(ω i, j ), ν(A i, j |A i )], ν(A i )], is valid only when the act f is comonotonic with its dynamic form, that we name “conditional certainty equivalent act”. 相似文献
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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.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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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 preferences on uncertain
payoffs and time contingent payoffs are derived from Ghirardato’s (1997) results. Conditional Choquet integrals are defined
by dynamic consistency (DC) requirements and conditional capacities are derived, under some conditions on information. In
contrast with other models referring to DC, ours does not collapse into a linear one because it violates a weak version of
consequentialism. 相似文献
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