Portfolio construction is the science of balancing reward and risk; it is at the core of modern finance. In this paper, we tackle the question of optimal decision-making within a Bayesian paradigm, starting from a decision-theoretic formulation. Despite the inherent intractability of the optimal decision in any interesting scenarios, we manage to rewrite it as a saddle-point problem. Leveraging the literature on variational Bayes (VB), we propose a relaxation of the original problem. This novel methodology results in an efficient algorithm that not only performs well but is also provably convergent. Furthermore, we provide theoretical results on the statistical consistency of the resulting decision with the optimal Bayesian decision. Using real data, our proposal significantly enhances the speed and scalability of portfolio selection problems. We benchmark our results against state-of-the-art algorithms, as well as a Monte Carlo algorithm targeting the optimal decision.

翻译：投资组合构建是平衡收益与风险的科学，是现代金融的核心。本文从决策理论框架出发，在贝叶斯范式下探讨最优决策问题。尽管任何有意义的场景中最优决策本质上难以精确求解，我们成功将其重写为鞍点问题。借助变分贝叶斯（VB）领域的研究成果，我们对原始问题提出一种松弛方法。这种新颖方法论催生出一个高效算法，该算法不仅性能优异，且具备可证明的收敛性。此外，我们针对所得决策与最优贝叶斯决策的统计一致性提供了理论分析。基于真实数据的实验表明，我们的方法显著提升了投资组合选择问题的求解速度与可扩展性。我们将实验结果与前沿算法以及针对最优决策的蒙特卡洛算法进行了基准比较。