Diversification Preferences in the Theory of Choice

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper studies axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion

When does aggregation reduce uncertainty aversion?

We study the problem of uncertainty sharing within a household: "risk sharing," in a context of Knightian uncertainty. A household shares uncertain prospects using a social welfare function. We characterize the social welfare functions such that the household is collectively less averse to uncertainty than each member, and satises the Pareto principle and an independence axiom. We single out the sum of certainty equivalents as the unique member of this family which provides quasiconcave rankings over risk-free allocations

Risk measurement with the equivalent utility principles.

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable at- tention in the financial mathematics literature. Mathematically, a risk measure is a mapping from a class of random variables defined on some measurable space to the (extended) real line. Economically, a risk measure should capture the preferences of the decision-maker. In incomplete financial markets, prices are no more unique but depend on the agents' attitudes towards risk. This paper complements the study initiated in Denuit, Dhaene & Van Wouwe (1999) and considers several theories for decision under uncertainty: the classical expected utility paradigm, Yaari's dual approach, maximin expected utility theory, Choquet expected utility theory and Quiggin rank-dependent utility theory. Building on the actuarial equivalent utility pricing principle, broad classes of risk measures are generated, of which most classical risk measures appear to be particular cases. This approach shows that most risk measures studied recently in the financial literature disregard the utility concept (i.e. correspond to linear utilities), causing some deficiencies. Some alternatives proposed in the literature are discussed, based on exponential utilities.Actuarial; Coherence; Decision; Expected; Market; Markets; Measurement; Preference; Premium; Prices; Pricing; Principles; Random variables; Research; Risk; Risk measure; Risk measurement; Space; Studies; Theory; Uncertainty; Utilities; Variables;

Risk, ambiguity, and the separation of utility and beliefs.

We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the non-expected utility models existing in the literature are special cases of it. Such separation is motivated by the view that tastes are constant, whereas beliefs change with new information. The model has a simple and natural axiomatization. Elsewhere (forthcoming) we show that it can be very helpful in the characterization of a notion of ambiguity aversion, as separating utility and beliefs allows to identify and remove aspects of risk attitude from the decision maker’s behavior. Here we show that the model allows to generalize several results on the characterization of risk aversion in betting behavior. These generalizations are of independent interest, as they show that some traditional results for subjective expected utility preferences can be formulated only in terms of binary acts.

NON-EXPECTED UTILITY THEORIES: WEIGHTED EXPECTED, RANK DEPENDENT, AND CUMULATIVE PROSPECT THEORY UTILITY

This paper discusses some of the failings of expected utility including the Allais paradox and expected utility's inadequate one dimensional characterization of risk. Three alternatives to expected utility are discussed at length; weighted expected utility, rank dependent utility, and cumulative prospect theory. Each alternative is capable of explaining Allais paradox type problems and permits more sophisticated multi dimensional risk preferences.Risk and Uncertainty,

An axiomatic model of 'cold feet'

Individuals often lose confidence in their prospects as they approach the "moment of truth." An axiomatic model of such individuals is provided. The model adapts and extends (by relaxing the Independence axiom) Gul and Pesendorfer's model of temptation and self-control to capture an individual who changes her beliefs so as to become more pessimistic as payoff time approaches. In a variation of the model, the individual becomes more optimistic at an ex post stage in order to feel better about her available options.pessimism, optimism, cold feet, temptation, self-control, moment of truth, temporal proximity, confidence

Cold feet

Individuals often lose confidence in their prospects as they approach the `moment of truth.' An axiomatic model of such individuals is provided. The model adapts and extends (by relaxing the Independence axiom) Gul and Pesendorfer's model of temptation and self-control to capture an individual who changes her beliefs so as to become more pessimistic as payoff time approaches. In a variation of the model, the individual becomes more optimistic at an ex post stage in order to feel better about her available options.Pessimism, optimism, cold feet, temptation, self-control, moment of truth, temporal proximity, confidence