Expected Utility Preferences for Contingent Claims and Lotteries

In Arrow’s seminal analysis of optimal risk bearing in which he introduced contingent claim securities, he assumed preferences were representable by a state independent Expected Utility function. Although the classic contingent claim setting assumes agents choose over contingent consumption vectors conditioned on a fixed set of probabilities, later work on information economics suggested that allowing probabilities to change across contingent claim spaces could be an interesting extension. However the set of axioms that are necessary and sufficient for the existence of an Expected Utility representation for the classic contingent claim space with a fixed set of probabilities does not ensure that this form utility extends across multiple contingent claim spaces. In this paper, we derive a set of axioms on preferences which are necessary and sufficient for the existence of an Expected Utility representation when probabilities change. We also consider the incremental axioms which are necessary and sufficient for Expected Utility preferences to extend to the classic lottery setting of von Neumann and Morgenstern, where agents choose not only over consumption vectors but also over probabilities vectors.