Calibration results for non-expected utility theories

Pre-print draft version dated July 24, 2006. Final version published by Wiley; available online at http://onlinelibrary.wiley.com/Rabin (2000) proved that a low level of risk aversion with respect to small gambles leads to a high, and absurd, level of risk aversion with respect to large gambles. Rabin’s arguments strongly depend on expected utility theory, but we show that similar arguments apply to general non-expected utility theories

Dual Betweenness

A key feature of the rank dependent model for decision making under risk is that the weighting of an outcome depends on its relative rank. This theory received numerous axiomatizations, however, all these sets of axioms need to make an explicit reference to the ranking of the outcomes. This situation is unsatisfactory, as it seems to be desirable to get the ranking property of this model as a consequence of the model, rather than as an assumption. Yaari [9] offered a special version of this model (called dual theory), where the utility function is linear. This paper offers a set of axioms implying a generalization of Yaari's dual theory, without making any reference to the order of the outcomes. The main axiom is called dual betweenness, which, unlike the usual case, is made on random variables rather than distribution functions. We thank SSHRCC and the Israel Institute of Business Research for financial support. y Faculty of Management, Tel Aviv University, Tel Aviv 6997..

On rational solutions of multicomponent and matrix KP hierarchies

We derive some rational solutions for the multicomponent and matrix KP hierarchies generalising an approach by Wilson. Connections with the multicomponent version of the KP/CM correspondence are discussed.Comment: 15 pages, no figure

Calibration results for incomplete preferences

In this work we demonstrate that incomplete expected utility preferences are susceptible to criticism similar to that addressed at their complete analogues: even a modest degree of risk aversion in the small is sufficient to imply extreme and unreasonable degree of risk aversion in the large. Our results thus shed doubt on the usefulness of incomplete expected utility preferences for practical and theoretical purposes

Virasoro constraints in Drinfeld-Sokolov hierarchies

We describe a geometric theory of Virasoro constraints in generalized Drinfeld-Sokolov hierarchies. Solutions of Drinfeld-Sokolov hierarchies are succinctly described by giving a principal bundle on a complex curve together with the data of a Higgs field near infinity. String solutions for these hierarchies are defined as points having a big stabilizer under a certain Lie algebra action. We characterize principal bundles coming from string solutions as those possessing connections compatible with the Higgs field near infinity. We show that tau-functions of string solutions satisfy second-order differential equations generalizing the Virasoro constraints of 2d quantum gravity.Comment: 28 page