Stochastic dominance for law invariant preferences: The happy story of elliptical distributions

Matteo Del Vigna ()
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Matteo Del Vigna: Dipartimento di Matematica per le Decisioni - Universita' degli Studi di Firenze

No 2012-08, Working Papers - Mathematical Economics from Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa

Abstract: We study the connections between stochastic dominance and law invariant preferences. Whenever the functional that represents preferences depends only on the law of the random variable, we shall look for conditions that imply a ranking of distributions. In analogy with the Expected Utility paradigm, we prove that functional dominance leads to first order stochastic dominance. We analyze in details the case of Dual Theory of Choice and Cumulative Prospect Theory, including all its distinctive features such as S-shaped value function, reversed S-shaped probability distortions and loss aversion. These cases can be seen as special examples of a more general scheme. We find necessary and sufficient conditions that imply preferences to depend only on the mean and variance of the lottery. Our main result is a characterization of such distributions that imply Mean-Variance preferences, namely the elliptical ones. In particular, we prove that under mild assumptions over the reference wealth, the prospect value of a portfolio depends only on its mean and variance if and only if the random assets' return are elliptically distributed. The analysis is of particular relevance for optimal portfolio choice, mutual fund separation and Capital Asset Pricing equilibria.

Keywords: Stochastic dominance; Cumulative Prospect Theory; Elliptical distributions; Mean-Variance analysis. (search for similar items in EconPapers)
JEL-codes: D03 D81 G11 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2012-10
New Economics Papers: this item is included in nep-ore and nep-upt
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