STOCHASTIC DOMINANCE

The concept of stochastic dominance is defined, and its relation to welfare, poverty, and income inequality explained. A brief discussion is provided of how statistical inference may be performed for hypotheses relating to stochastic dominance.

Multivariate concave and convex stochastic dominance

Stochastic dominance permits a partial ordering of alternatives (probability distributions on consequences) based only on partial information about a decision maker’s utility function. Univariate stochastic dominance has been widely studied and applied, with general agreement on classes of utility functions for dominance of different degrees. Extensions to the multivariate case have received less attention and have used different classes of utility functions, some of which require strong assumptions about utility. We investigate multivariate stochastic dominance using a class of utility functions that is consistent with a basic preference assumption, can be related to well-known characteristics of utility, and is a natural extension of the stochastic order typically used in the univariate case. These utility functions are multivariate risk averse, and reversing the preference assumption allows us to investigate stochastic dominance for utility functions that are multivariate risk seeking. We provide insight into these two contrasting forms of stochastic dominance, develop some criteria to compare probability distributions (hence alternatives) via multivariate stochastic dominance, and illustrate how this dominance could be used in practice to identify inferior alternatives. Connections between our approach and dominance using different stochastic orders are discussed.decision analysis: multiple criteria, risk; group decisions; utility/preference: multiattribute utility, stochastic dominance, stochastic orders

Poverty, Inequality and Stochastic Dominance, Theory and Practice: Illustration with Burkina Faso Surveys

In this paper we provide a set of rules that can be used to check poverty or inequality dominance using discrete data. Existing theoretical rules assumes continuity in incomes or in percentiles of population. In reality, with the form of household surveys, this continuity does not exist. However, the said discontinuity can be exploited in testing the stochastic dominance. Moreover, in this paper, we proprose the stochastic dominance conditions that take into account the statistical robustness in testing the stochastic dominance. Findings of this paper are illustrated using the Burkina Faso's household surveys for the years of 1994 and 1998.Stochastic Dominance, Poverty, Inequality

SHADOW PRICE IMPLICATIONS OF SEVERAL STOCHASTIC DOMINANCE CRITERIA

Stochastic dominance criteria can be, but seldom are explicitly, applied to problems having continuous variables. A previously developed model is modified to facilitate exploration of sets of shadow price vectors for decreasing (non-increasing) absolute risk aversion stochastic dominance (DSD), a combination, TGSD, of third degree stochastic dominance (TSD) and generalized stochastic dominance (GSD) and a combination, DGSD, of DSD and GSD. The model is illustrated by applying it to two risk efficient (primal) solutions of a problem by Anderson, Dillon and Hardaker. For each of the two primal solutions and, where relevant, three risk aversion coefficient intervals, selected aspects of the sets of shadow price vectors consistent with TSD, DSD, TGSD and DGSD are compared with each other and with sets of shadow price vectors consistent with GSD and second degree stochastic dominance (SSD).Demand and Price Analysis,

Probabilistic Sophistication, Second Order Stochastic Dominance, and Uncertainty Aversion

We study the interplay of probabilistic sophistication, second order stochastic dominance, and uncertainty aversion, three fundamental notions in choice under uncertainty. In particular, our main result, Theorem 2, characterizes uncertainty averse preferences that satisfy second order stochastic dominance, as well as uncertainty averse preferences that are probabilistically sophisticated.Probabilistic Sophistication; Second Order Stochastic Dominance; Uncertainty Aversion; Unambiguous Events; Subjective Expected Utility

PREFERENCE RELATIONS IN RANKING MULTIVALUED ALTERNATIVES USING STOCHASTIC DOMINANCE: CASE OF THE WARSAW STOCK EXCHANGE

This study used stochastic dominance tests for ranking alternatives under ambiguity, to build an efficient set of assets for a different class of investors. We propose a two step procedure: first test for multivalued stochastic dominance and next calculate the value of preference relations. The empirical part of paper was set by results from the Warsaw Stock Exchange. In decision situations we should compare many alternatives. When alternatives take uncertain character we can evaluate the performance of alternatives only in a probabilistic way. In finance, for example, problems arise with stock selection when we needs to compare return distributions. The construction of a local preference relation already requires the comparison of two probability distributions. Stochastic dominance is based on a model of risk averse preferences, which was done by Fishburn (1964) and was extended by Levy and Sarnat (1984, 1992). When we verified some of the stochastic dominance we also observed additionally that the dominance is not equivalent. We present preference relations that could help globally ranking alternatives. When one of the type of stochastic dominance is verified, we can calculate the degree of the decision maker preference by using the preference relation d. The degree of preference decreases progressively as we go from the dominance FSD to the dominance TSD. This degree of credibility of the preference relation will allow us to know the nature of the preference relation between two alternatives X and Y basis of the characteristic obtained for three functions by type of dominance, in the case of each dominance. It is easy to apply this relation for rank multivalued outcomes, which we firstly rank by multivalued stochastic dominance.

Apportioning of Risks via Stochastic Dominance

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable Xi dominates Yi via ith-order stochastic dominance for i = M,N. We show that the 50-50 lottery [XN + YM, YN + XM] dominates the lottery [XN + XM, YN + YM] via (N + M)th-order stochastic dominance. The basic idea is that a decision maker exhibiting (N + M)th-order stochastic dominance preference will allocate the state-contingent lotteries in such a way as not to group the two "bad" lotteries in the same state, where "bad" is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher order risk effects, such as precautionary effects and tempering effects.downside risk, precautionary effects, prudence, risk apportionment, risk aversion, stochastic dominance, temperance

Elitism and Stochastic Dominance

Stochastic dominance has typically been used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adpations be made. We apply in the paper the stochastic dominance approach to the measurment of elitism which may be considered the opposite of egalitarianism. While the usual stochastic dominance quasi-orderings attach more value to more equal and more efficient distributions, our criteria ensure that the more unequal and the more the efficient the distribution, the higher it is ranked. two instances are provided by (i) comparisons of scientific performance across institutions like universities or departments and (ii) comparisons of affluence as opposed to poverty across countries.Decumulative distribution functions; Stochastic dominance; Regressive transfers; Elitism; Scientific Performance; Affluence

Elitism and Stochastic Dominance

Stochastic dominance has been typically used with a special emphasis on risk and in-equality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance ap-proach goes far beyond risk and inequality measurement provided suitable adaptations be made. We apply in the paper the stochastic dominance approach to the measurement of elitism which may be considered the opposite of egalitarianism. While the usual stochastic dominance quasi-orderings attach more value to more equal and more effi-cient distributions, our criteria ensure that, the more unequal and the more efficient the distribution, the higher it is ranked. Two instances are provided by (i) comparisons of scientific performance across institutions like universities or departments, and (ii) com-parisons of affluence as opposed to poverty between countries.Decumulative Distribution Functions, Stochastic Dominance, Regressive Transfers, Elitism, Scientific Performance, Affluence