Almost stochastic dominance via optimal transport

Battle Count: 75

Stochastic dominance is a fundamental concept in quantitative finance for comparing portfolios, assets, and strategies. The paper's framework for multivariate almost stochastic dominance via optimal transport is directly applicable to comparing multivariate return distributions, benchmarking trading strategies against indices, and risk assessment. The robustness results are relevant for practical applications where distribution estimates are noisy. However, the paper is primarily theoretical and does not directly address trading strategy development or backtesting. The connection to the Omega ratio (Keating and Shadwick, 2002) in the univariate case provides a direct link to performance measurement in finance.

The theoretical framework requires understanding of optimal transport, quasi-pseudo-metrics, and Kantorovich duality. The Auction Algorithm implementation is well-documented (Bertsekas 1990) and scales linearly in dimension d, making it practical for moderate dimensions. The main computational challenge is solving the OT problem for large-scale empirical distributions. The paper provides clear formulas for γ* computation and the test function characterization. For the specific R^d case with c(x,y)=Σ(x_i-y_i)+, the problem reduces to a linear assignment problem solvable by the Auction Algorithm.

The paper provides a clear algorithmic framework (Auction Algorithm from Bertsekas 1990), explicit cost functions, and uses publicly available satellite data (global horizontal irradiation) for the sunshine example. The bivariate Gaussian example is fully specified with parameters. However, no code repository is provided, and the theoretical proofs require substantial mathematical background to verify independently.