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.