Economic Comparisons of Alternative Theories of Stochastic Dominance

42 Pages Posted: 18 Oct 2022 Last revised: 30 Mar 2023

See all articles by David P. Brown

David P. Brown

University of Wisconsin - Madison - Department of Finance, Investment and Banking

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

Brown, David P., Economic Comparisons of Alternative Theories of Stochastic Dominance (June 13, 2022). Available at SSRN: https://ssrn.com/abstract=4242949 or http://dx.doi.org/10.2139/ssrn.4242949

David P. Brown (Contact Author)

University of Wisconsin - Madison - Department of Finance, Investment and Banking ( email )

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