2026/05/28 by Miquel Noguer i Alonso · 1 voice
Economics, Econometrics and Finance · #q-fin.PM
Classical portfolio optimization treats expected returns, covariances, and allocations as deterministic. Modern practice replaces at least one by a distribution: a posterior over parameters, a law of future returns, a stochastic allocation policy, or a distributional-robustness set. We call distributional portfolio optimization (DPO) the unified framework in which weights, returns, and parameters are all modeled as probability measures, organized around the joint coupling Gammatheta(dw,dr) and its marginal triple (W,R,P). The contribution is synthetic and structural: we organize Bayesian, robust, chance-constrained, stochastic-allocation, and distributional reinforcement-learning portfolio methods through this coupling and prove boundary results connecting them, including a portfolio specialization of Wasserstein-CVaR duality, a static no-randomization theorem, a Bayesian credible-radius calibration of Wasserstein DRO, a Gaussian-isotropic second-order conservatism bound, a conditional two-sided rate W1 = Theta(n-(1+alpha)/2) governed by the local boundary Holder exponent alpha in [0,1], and a risk-shifted distributional Bellman contraction. A controlled experiment shows that across factor models at K in 10,25,50, the credible-radius rule lands within 3-7 bp of the oracle out-of-sample tail risk and beats a 24-month validation-tuned radius while spending no validation data. On a K=25 DJIA backtest, equal-weight, no-view Black-Litterman, and Ledoit-Wolf shrinkage attain higher Sharpe than every distributional method; the operational claim is therefore confined to calibration-without-validation and turnover, not raw-return dominance.