General linear formulations of stochastic dominance criteria

•We develop linear formulations of general Nth order stochastic dominance criteria.•Our primal formulations use a piece-wise polynomial representation of utility.•Our dual formulations use lower partial moments and co-lower partial moments.•An empirical application analyses the passive US stock mark...

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Bibliographic Details
Published in:European journal of operational research Vol. 230; no. 2; pp. 321 - 332
Main Authors: Post, Thierry, Kopa, Miloš
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.10.2013
Elsevier
Elsevier Sequoia S.A
Subjects:
Criteria
Derivatives
Dominance
Formulations
Linear programming
Markets
Mathematical problems
Non-satiation
Polynomials
Probability distribution
Prudence
Raw materials
Risk aversion
Securities markets
Stochastic dominance
Stochastic models
Stochasticity
Studies
Temperance
Utility theory
Risk aversion
Prudence
Temperance
Stochastic dominance
Utility theory
Non-satiation
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•We develop linear formulations of general Nth order stochastic dominance criteria.•Our primal formulations use a piece-wise polynomial representation of utility.•Our dual formulations use lower partial moments and co-lower partial moments.•An empirical application analyses the passive US stock market portfolio.•The passive portfolio seems dominated by actively managed alternatives. We develop and implement linear formulations of general Nth order stochastic dominance criteria for discrete probability distributions. Our approach is based on a piece-wise polynomial representation of utility and its derivatives and can be implemented by solving a relatively small system of linear inequalities. This approach allows for comparing a given prospect with a discrete set of alternative prospects as well as for comparison with a polyhedral set of linear combinations of prospects. We also derive a linear dual formulation in terms of lower partial moments and co-lower partial moments. An empirical application to historical stock market data suggests that the passive stock market portfolio is highly inefficient relative to actively managed portfolios for all investment horizons and for nearly all investors. The results also illustrate that the mean–variance rule and second-order stochastic dominance rule may not detect market portfolio inefficiency because of non-trivial violations of non-satiation and prudence.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2013.04.015