Traditional portfolio optimization typically relies on a single fitted return distribution, thus ignores non-normality and uncertainty across distributional states. Mean–variance–ambiguity (MVA) models, motivated by the smooth-ambiguity preferences of Klibanoff, Marinacci, and Mukerji (2005) and the KMM-to-MVA Arrow–Pratt reduction of Maccheroni, Marinacci, and Ruffino (2013), extend conventional risk penalties to account for distributional uncertainty, but they missed how state-conditional return distributions affect portfolio optimization stability. We develop Deep Mean–Variance–Ambiguity (Deep MVA) to resolve this gap by learning state-conditional return distributions and embedding the resulting conditional information loss into the ambiguity penalty. 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 optimization. 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 state-conditional distribution 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.

We develop a signaling game model of investment to explore the effects of ambiguity aversion on corporate equilibrium strategies, investment dynamics, and financing decisions in incomplete markets with asymmetric information. Our analysis shows that volatility ambiguity aversion has a similar but more pronounced effect than asymmetric information, leading to higher financing costs, lower investment probabilities, and a greater likelihood of non-participation in investment. Importantly, volatility ambiguity aversion exhibits an amplifier effect, magnifying financing costs, adverse selection costs, and distortion in investment choices under asymmetric information. This increased ambiguity aversion raises the chances of inefficient separating and pooling equilibria, resulting in notable welfare losses. These findings highlight the significant impact of ambiguity aversion on strategic decision-making and equilibrium outcomes in investment, particularly in settings marked by information asymmetry and incomplete markets.

Based on the expected utility under uncertain probability distribution, we explore whether the ambiguity of individual stocks is priced in China’s A-share market and the mechanism behind the ambiguity premium phenomenon. Theoretically, when the asset price is in a specific price range, investors with ambiguity aversion do not participate in the transaction of the asset. As the ambiguity of assets increases, investors with high ambiguity aversion withdraw from the market, and investors with low ambiguity aversion remain in the market (the limited market participation phenomenon); investors who remain in the market due to lower ambiguity aversion are also willing to accept a low ambiguity premium. Empirically, we use "the volatility of the distributions of daily stock returns within a month" to measure monthly ambiguity; and find that (1) the equal-weighted average returns of the most ambiguous portfolios (top 20%) are significantly lower 1.38% than those of the least ambiguous portfolios (bottom 20%); (2) ambiguity still significantly negatively affects the cross-sectional stock return after controlling for common firm characteristics; (3) the higher the ambiguity, the lower the future trading activity, the empirical results are consistent to the theoretical predictions. Those findings reveal the mechanism of the negative ambiguity premium in the A-share market, provide new ideas for further building a factor pricing model suitable for the A-share market, and provide a fresh perspective for preventing systemic financial risk.

Based on the expected utility under uncertain probability distribution, we explore whether the ambiguity of individual stocks is priced in China’s A-share market and the mechanism behind the ambiguity premium phenomenon. Theoretically, when the asset price is in a specific price range, investors with ambiguity aversion do not participate in the transaction of the asset. As the ambiguity of assets increases, investors with high ambiguity aversion withdraw from the market, and investors with low ambiguity aversion remain in the market (the limited market participation phenomenon); investors who remain in the market due to lower ambiguity aversion are also willing to accept a low ambiguity premium. Empirically, we use "the volatility of the distributions of daily stock returns within a month" to measure monthly ambiguity; and find that (1) the equal-weighted average returns of the most ambiguous portfolios (top 20%) are significantly lower 1.38% than those of the least ambiguous portfolios (bottom 20%); (2) ambiguity still significantly negatively affects the cross-sectional stock return after controlling for common firm characteristics; (3) the higher the ambiguity, the lower the future trading activity, the empirical results are consistent to the theoretical predictions. Those findings reveal the mechanism of the negative ambiguity premium in the A-share market, provide new ideas for further building a factor pricing model suitable for the A-share market, and provide a fresh perspective for preventing systemic financial risk.