Stochastic dominance for law invariant preferences: The happy story of elliptical distributions
AbstractWe 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.
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Bibliographic InfoPaper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Mathematical Economics with number 2012-08.
Length: 26 pages
Date of creation: Oct 2012
Date of revision:
Stochastic dominance; Cumulative Prospect Theory; Elliptical distributions; Mean-Variance analysis.;
Find related papers by JEL classification:
- D03 - Microeconomics - - General - - - Behavioral Microeconomics; Underlying Principles
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-11-03 (All new papers)
- NEP-ORE-2012-11-03 (Operations Research)
- NEP-UPT-2012-11-03 (Utility Models & Prospect Theory)
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