distributionally robust portfolio optimization

This study addresses the limited robustness of traditional optimization approaches in asset-liability management (ALM) for pension funds and other financial institutions, stemming from uncertainty in the distribution of future returns. To overcome this challenge, the paper constructs and systematically compares three types of distributionally robust optimization (DRO) ambiguity sets: mixture-of-discrete scenarios, box uncertainty sets over discrete distributions, and Wasserstein metric-based ambiguity sets. Using real-world data from a Canadian pension plan, the authors provide the first empirical evidence that both Wasserstein and box ambiguity sets significantly outperform mixture DRO and conventional stochastic programming in ensuring long-term solvency while enhancing investment returns. These findings highlight the superior performance and practical relevance of Wasserstein- and box-based DRO frameworks in ALM applications.

This paper addresses path-dependent distributionally robust stochastic control under non-concave loss functions over a finite horizon, aiming to mitigate model misspecification risk in extreme scenarios such as financial crises. We establish the first dynamic programming principle applicable to non-concave objectives and propose a unified, path-dependent ambiguity set framework compatible with both Wasserstein balls and parametric distribution families. Furthermore, we introduce a novel robust hedging paradigm for financial derivatives that explicitly accommodates bilateral, asymmetric preferences of buyers and sellers, and implement fully data-driven ambiguity set construction. Empirical results demonstrate that the proposed strategy significantly outperforms delta hedging and non-robust methods based on the empirical measure under extreme market conditions, markedly enhancing hedging robustness. Our core contributions lie in (i) a theoretical breakthrough—dynamic programming for non-concave robust optimization; (ii) methodological innovation—path-dependent and data-driven ambiguity modeling; and (iii) financial application advancement—robust hedging under asymmetric preference structures.

This paper addresses robust portfolio optimization under uncertainty in mean–covariance estimates. We propose a novel robust risk-measurement framework based on the Gelbrich distance—introduced for the first time in the mean–covariance space—to quantify parameter ambiguity while incorporating prior structural information about the underlying distribution. Theoretically, we prove that, under mainstream risk measures including Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), the resulting robust optimization problem is equivalent to a regularized Markowitz model with a closed-form penalty term. Our method integrates optimal transport theory, convex analysis, and robust optimization, ensuring both statistical robustness and computational efficiency. Compared with existing approaches, our framework unifies treatment across multiple risk measures, supports large-scale real-time optimization, and significantly enhances model generalizability and practical applicability.

This paper addresses model misspecification, transaction costs, and partial observability—key sources of uncertainty in real-world financial markets. Method: We propose a robust utility optimization framework based on Generative Adversarial Networks (GANs), formulating a neural-network-based minimax game between an investor and an adversarial market. Under partial observability—relying solely on historical asset prices—we approximate the worst-case utility maximization. This is the first application of the GAN paradigm to robust portfolio decision-making, accommodating arbitrary continuous utility functions. Contribution/Results: We theoretically establish that path-dependent strategies offer no advantage over Markovian ones. Empirically, our approach matches benchmark optimal policies when known, and significantly outperforms all baselines in the absence of prior optimal solutions. The learned policies exhibit strong generalization and are directly deployable in practice.

Sequential decision-making under model uncertainty remains challenging, particularly when prior knowledge is limited and posterior distributions are complex. Method: This paper proposes DRO-BAS, a distributionally robust optimization (DRO) framework grounded in Bayesian posterior inference. It constructs two novel ambiguity sets—posterior expectation–based and posterior predictive–based—enabling unified modeling across the entire conjugate exponential family. The framework leverages strong duality theory to ensure computational tractability and supports efficient single-stage optimization. Contributions/Results: DRO-BAS theoretically guarantees strong duality and finite-dimensional reformulation, yielding closed-form or convex optimization solutions. Empirically, it achieves Pareto dominance over existing Bayesian DRO methods on the Newsvendor problem and significantly accelerates computation—while maintaining comparable robustness—in portfolio optimization. All claims are validated on standard benchmarks, integrating distributionally robust optimization, Bayesian inference, and strong duality theory.

This study addresses the neglect of parameter and return uncertainty in traditional portfolio optimization by proposing a Distributional Portfolio Optimization (DPO) framework. The approach unifies portfolio weights, asset returns, and model parameters under a joint probability measure, integrating Bayesian inference, distributionally robust optimization (DRO), chance constraints, and distributional reinforcement learning. Key theoretical contributions include a Wasserstein–CVaR duality, a no-randomization theorem, Bayesian credible-radius-calibrated Wasserstein DRO, Gaussian conservative bounds, and a distributional Bellman contraction property under risk translation. Empirically, the method achieves near-oracle tail risk performance in factor models—exceeding it by only 3–7 basis points—without requiring a validation set. However, in out-of-sample backtests on the DJIA, it does not significantly outperform benchmark strategies such as equal weighting, Black–Litterman, or Ledoit–Wolf in terms of Sharpe ratio.

This study addresses the decision-making risk arising from uncertainty in loss distributions within insurance contract design. From the policyholder’s perspective, it constructs an asymmetric distributional ambiguity set using a Bregman–Wasserstein (BW) ball to capture asymmetric penalties for deviations from a reference distribution. Under α-maxmin preferences with a Value-at-Risk (VaR) constraint and worst-case convex distortion risk measures, the authors combine Lagrangian methods with a refined duality argument to derive, for the first time, closed-form solutions for both the optimal indemnity function and the worst-case distribution within a robust insurance demand framework. Numerical experiments demonstrate that the asymmetry inherent in the BW divergence critically shapes the structure of optimal insurance contracts.

This study addresses the loss incurred by Bayesian investors when asset drifts are unknown and the observation model may be misspecified. The authors develop a robust investment framework in path space by integrating Kalman–Bucy filtering with mean–variance optimization, incorporating adversarial perturbations penalized by relative entropy to account for potential misspecification of the price distribution. They innovatively reveal the joint perturbation effect on wealth and belief processes driven by a common Brownian motion and prove that value scaling exactly preserves the affine structure of the optimal strategy. The resulting closed-form robust policy incurs, at leading order, only half the loss variance of its non-robust counterpart and automatically trims large positions through third-order corrections, thereby guaranteeing finite losses and controlled risk exposure.

This study addresses dynamic mean-variance portfolio optimization in a continuous-time multi-asset Black-Scholes market where investors face uncertainty about asset return drifts and exhibit ambiguity aversion. By adopting the variance decomposition criterion of Maccheroni et al., the framework explicitly distinguishes between market risk and model ambiguity. Integrating Bayesian learning, stochastic control, and mean-variance optimization, the authors develop a tractable dynamic decision-making framework that accommodates parameter uncertainty. Within a class of adaptive learning strategies, they derive the optimal investment policy in closed form. Numerical experiments demonstrate that ambiguity aversion substantially reduces allocations to risky assets, underscoring the critical influence of model uncertainty on investor behavior.