Stochastic Dominance Efficiency Tests under Diversification

This paper focuses on Stochastic Dominance (SD) efficiency in a finite empirical panel data. We analytically characterize the sets of unsorted time series that dominate a given evaluated distribution by the First, Second, and Third order SD. Using these insights, we develop simple Linear Programming and 0-1 Mixed Integer Linear Programming tests of SD efficiency. The advantage to the earlier efficiency tests is that the proposed approach explicitly accounts for diversification. Allowing for diversification can both improve the power of the empirical SD tests, and enable SD based portfolio optimization. A simple numerical example illustrates the SD efficiency tests. Discussion on the application potential and the future research directions concludes.