This paper develops a quantitative framework to assess the robustness of Bayes-optimal decisions in finite decision problems under model uncertainty. We introduce two complementary stability notions for acts: the robustness radius, measuring the largest perturbation of a reference prior under which an act remains Bayes-optimal, and the contamination need, quantifying the minimal perturbation required for an act to become Bayes-optimal under some nearby prior. Both concepts are characterized via linear programming formulations and computed efficiently using bisection methods exploiting monotonicity properties. Building on these stability measures, we propose a cost-adjusted stability criterion that integrates robustness considerations with act-specific selection costs, yielding a parametric family of decision rules indexed by a regularization parameter. We analyze how optimal act selection evolves along this parameter and derive selection paths that reveal structural transitions between stability-driven and cost-driven regimes. The framework is applied to a portfolio choice problem under uncertainty between different economic regimes. Concretely, using data on historical ETF returns, we compute robustness and contamination profiles for six portfolio strategies and analyze their behavior under heterogeneous belief specifications. The results illustrate that robustness-based selection refines classical expected utility by accounting for prior misspecification.

翻译：本文针对有限决策问题中模型不确定性下的贝叶斯最优决策，建立了一套量化鲁棒性评估框架。我们提出了行为的两种互补稳定性概念：鲁棒半径——衡量使行为保持贝叶斯最优性的参考先验最大扰动幅度；污染需求——量化在邻近先验下使某行为达到贝叶斯最优所需的最小扰动量。这两种概念均通过线性规划形式刻画，并利用单调性性质采用二分法实现高效计算。基于这些稳定性度量，我们提出成本调整稳定性准则，将鲁棒性考量与行为专属选择成本相结合，从而产生由正则化参数索引的参数化决策规则族。我们分析了最优行为选择沿该参数的演化规律，导出揭示稳定性驱动与成本驱动模式间结构转换的选择路径。将该框架应用于不同经济体制不确定性下的投资组合选择问题：具体而言，基于历史ETF收益率数据，我们计算六种组合策略的鲁棒性与污染剖面，并分析其在异质性信念设定下的行为特征。结果表明，基于鲁棒性的选择通过考虑先验设定偏误，优化了经典期望效用准则。