Portfolio optimization with robust stochastic dominance testing: A genetic algorithm approach

This paper introduces the s-RSD model, a robust portfolio optimization framework that generalizes stochastic dominance constraints of any given order s by allowing for outlier disturbances within the bounds of a Kolmogorov-Smirnov like statistical test critical value at a chosen significance level α. By generalizing strict dominance and allowing controlled, statistically insignificant violations, the model robustly balances return maximization with risk control. Genetic Algorithm is employed to solve the resulting nonlinear optimization problem, accommodating cardinality constraints and weight bounds, and achieving rapid convergence relative to exact solvers. Empirical analysis was performed on S&P 500 data under bearish, neutral, and bullish market conditions, demonstrating that, with appropriate tuning of the stochastic dominance order and significance level α, it is possible to reduce losses during downturns, enhance returns in stable markets, and realize outsized gains. Investor-specific tailoring of the risk-return trade-off is enabled by the adjustable parameters s and α. A flexible and powerful tool for modern portfolio management is provided by the proposed methodology.