Higher-Degree Stochastic Dominance Optimality and Efficiency

33 Pages Posted: 26 Jan 2016 Last revised: 12 Mar 2017

See all articles by Yi Fang

Yi Fang

Jilin University (JLU) - Center for Quantitative Economics

Thierry Post

Graduate School of Business of Nazarbayev University

Date Written: March 9, 2017

Abstract

We characterize a range of Stochastic Dominance relations by means of finite systems of convex inequalities. For 'SD optimality' of degree N=1, 2, 3, 4 and 'SD efficiency' of degree N=2, 3, 4, 5, we obtain exact systems that can be implemented using Linear Programming or Convex Quadratic Programming. For SD optimality of degree N>=5 and SD efficiency of degree N>=6, we obtain necessary conditions. Our analysis leads to higher accuracy than existing necessary and approximate conditions for higher-degree relations if the partition of the outcomes domain is coarse. In addition, we use separate model variables for the values of the derivatives of all relevant orders at all relevant outcome levels, which allows for preference restrictions beyond the standard sign restrictions. Our systems of inequalities can be interpreted in terms of piecewise polynomial utility functions with a number of pieces that increases with the number of outcomes (T) and the degree of SD (N).

Keywords: Stochastic Dominance, Expected Utility, Portfolio choice, Linear Programming, Convex Quadratic Programming

JEL Classification: B40, C61, D81

Suggested Citation

Fang, Yi and Post, Thierry, Higher-Degree Stochastic Dominance Optimality and Efficiency (March 9, 2017). Available at SSRN: https://ssrn.com/abstract=2722244 or http://dx.doi.org/10.2139/ssrn.2722244

Yi Fang (Contact Author)

Jilin University (JLU) - Center for Quantitative Economics ( email )

Changchun, Jilin 130012
China

Thierry Post

Graduate School of Business of Nazarbayev University ( email )

53 Kabanbay Batyra Avenue
Astana, 010000
Kazakhstan

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