Abstract. Let E be a class of event. Conditionally Expected Utility decision makers are decision makers whose conditional preferences %E, E 2 E, satisfy the axioms of Subjective Expected Utility theory (SEU). We extend the notion of unconditional preference that is conditionally EU to unconditional preferences that are not necessarily SEU. We give a representation theorem for a class of such preferences, and show that they are Invariant Bi-separable in the sense of Ghirardato et al. [7]. Then, we consider the special case where the unconditional preference is itself SEU, and compare our results with those of Fishburn [6].
Abstract. Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., [23]). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then there exist optimal monotonic indemnity schedules. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., [25]). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow [5] on the optimality of the deductible indemnity schedule.
The paper provides a notion of measurability for Multiple Prior Models characterized by nonatomic countably additive priors. A notable feature of our definition of measurability is that an event is measurable if and only if it is unambiguous in the sense of Ghirardato, Maccheroni and Marinacci [6]. In addition, the paper contains a thorough description of the basic properties of the family of measurable/unambiguous sets, of the measure defined on those and of the dependence of the class of measurable sets on the set of priors. The latter is obtained by means of an application of Lyapunov’s convexity theorem. Copyright Springer-Verlag Berlin/Heidelberg 2005Ambiguous events, Multiple priors, Lyapunov’s convexity theorem.,
We study the properties associated to various de…nitions of ambiguity ([8], [9], [18] and [23]) in the context of Maximin Expected Utility (MEU). We show that each de…nition of unambiguous events produces certain restrictions on the set of priors, and completely characterize each de…nition in terms of the properties it imposes on the MEU functional. We apply our results to two open problems. First, in the context of MEU, we show the existence of a fundamental incompatibility between the axiom of "Small unambiguous event continuity" ([8]) and the notions of unambiguous event due to Zhang [23] and Epstein-Zhang [8]. Second, we show that, in the context of MEU, the classes of unambiguous events according to either Zhang [23] or Epstein-Zhang [8] are always-systems. Finally, we reconsider the various de…nitions in light of our …ndings, and identify some new objects (Z-…lters and EZ-…lters) corresponding to properties which, while neglected in the current literature, seem relevant to us.
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