研究

Traditional portfolio optimization treats the expected return law as known, exposing the portfolio to distributional disagreement and lost state-specific information.

We develop Deep Mean-Variance-Ambiguity (Deep MVA), building on the smooth-ambiguity preferences of Klibanoff, Marinacci, and Mukerji (2005) and the KMM-to-MVA Arrow–Pratt reduction of Maccheroni, Marinacci, and Ruffino (2013). The resulting local certainty equivalent combines reduced-law mean–variance risk with a quadratic penalty for second-order disagreement.

Conditional-mixture state resolution yields a Deep ambiguity covariance equal to the Traditional ambiguity covariance plus a positive-semidefinite state-feature increment. This increment is the conditional L2 loss from averaging state-specific distributions before allocation.

On compact convex feasible sets, we show that the state-resolving program has stronger ambiguity-relevant curvature, lower mean-input sensitivity, and a unique global solution under restricted positive curvature or a common ridge; its projected iterations converge linearly.

An LSTM-MDN learns non-normal densities from 60-minute bars, and Probability and VoV scores enter weekly MVA, with GARCH_Resid as a comparator. Tests on the SSE 50, CSI 300, and CSI 500 universes from 2017–2025 find statistically significant Sharpe out-of-sample improvements over Traditional MVA and MVO across all three universes and ambiguity specifications.