Economic Comparisons of Alternative Theories of Stochastic Dominance
42 Pages Posted: 18 Oct 2022 Last revised: 30 Mar 2023
Date Written: June 13, 2022
Abstract
The theory of stochastic dominance applied to financial decisions associates classes of investors with classes of gambles (random payoffs). Each investor resides in a class of mixed risk averters (MRA). Pairs of gambles, say, X and Y are classified by moment inequalities and distributional inequalities. This paper represents these inequalities as comparisons of preference within a generating class of investors B with parametric utility functions, B⊂MRA; gamble X dominates Y if and only if members of B unanimously prefer X over Y. Generating classes lead to economic comparisons of three alternative theories of dominance. One comparison demonstrates a tradeoff between the moment and distributional inequalities. A second compares theories of dominance within finance and social welfare. These results caution those who might use the test statistics developed for social welfare in their studies of financial data
Keywords: Stochastic dominance, representation theorem, mixed risk averters
JEL Classification: D60, D63, D81, G10, O57
Suggested Citation: Suggested Citation