可证明的高维Wasserstein鲁棒投资组合优化
Certified High-Dimensional Wasserstein Robust Portfolio Optimization
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中文总结 AI 辅助
针对高维Wasserstein分布鲁棒投资组合优化，提出可证明的多项式规模线性规划近似方法，经实验验证可实现476项资产月度再平衡及1000项资产的计算可扩展性。
中文摘要 AI 辅助
我们开发了一种可证明的、可扩展的高维Wasserstein分布鲁棒投资组合优化近似方法。对于一阶Wasserstein模糊下的期望效用最大化，标准对偶性会产生一个半无限凸规划。对于在一范数基础度量下具有箱型支撑的仅多头投资组合，精确的样本特定顶点重构提供了指数规模的计算基准。随后，我们用支撑超平面对效用进行上控制，并对偶化支撑子问题，得到了在紧多面体支撑上的有限超平面对偶形式。在一范数基础度量和多面体投资组合约束下，该形式是一个多项式规模的线性规划。统一的效用近似误差同时界定了原鲁棒问题的鲁棒值误差和近最优性差距。实验验证了该可证明近似方法，并展示了476项资产的月度再平衡以及对1000项资产的计算可扩展性。
英文摘要
We develop a certified, scalable approximation for high-dimensional Wasserstein distributionally robust portfolio optimization. For expected-utility maximization under order-one Wasserstein ambiguity, standard duality yields a semi-infinite convex program. For long-only portfolios with box support under the one-norm ground metric, an exact sample-specific vertex reformulation provides an exponential-size computational benchmark. We then majorize the utility by supporting hyperplanes and dualize the support subproblems, obtaining a finite hyperplane--dual formulation over compact polyhedral supports. Under the one-norm ground metric and polyhedral portfolio constraints, this formulation is a polynomial-size linear program. The uniform utility-approximation error bounds both the robust-value error and the near-optimality gap for the original robust problem. Experiments validate the certified approximation and demonstrate monthly 476-asset rebalancing and computational scalability to 1,000 assets.
