Stochastic dominance for law invariant preferences: The happy story of elliptical distributions
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.
|Date of creation:||Oct 2012|
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- Levy, Haim & Wiener, Zvi, 1998. "Stochastic Dominance and Prospect Dominance with Subjective Weighting Functions," Journal of Risk and Uncertainty, Springer, vol. 16(2), pages 147-63, May-June.
- Fortin, Ines & Hlouskova, Jaroslava, 2011.
"Optimal asset allocation under linear loss aversion,"
Journal of Banking & Finance,
Elsevier, vol. 35(11), pages 2974-2990, November.
- Fortin, Ines & Hlouskova, Jaroslava, 2010. "Optimal Asset Allocation Under Linear Loss Aversion," Economics Series 257, Institute for Advanced Studies.
- Baucells Alibés Manel & Heukamp Franz H., 2007.
"Stochastic Dominance and Cumulative Prospect Theory,"
201061, Fundacion BBVA / BBVA Foundation.
- Manel Baucells & Franz H. Heukamp, 2006. "Stochastic Dominance and Cumulative Prospect Theory," Management Science, INFORMS, vol. 52(9), pages 1409-1423, September.
- Carlier Guillaume & Dana Rose-Anne, 2006. "Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 26, July.
- Kahneman, Daniel & Tversky, Amos, 1979.
"Prospect Theory: An Analysis of Decision under Risk,"
Econometric Society, vol. 47(2), pages 263-91, March.
- Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
- Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
- Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
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