Higher-Degree Stochastic Dominance Optimality and Efficiency

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)