Generalized Robust Optimization using the Notion of Set-Valued Probability
提出一种基于集值概率框架的鲁棒性新概念，通过标量化技术推导最优性条件，并建立广义凸性和稳定性条件，为金融投资组合和风险度量等领域的决策优化提供工具。
We propose a novel concept of robustness grounded in the framework of set-valued probabilities, offering a unified and versatile approach to tackling challenges associated with the statistical estimation of uncertain or unknown probabilities. By employing scalarization techniques for set-valued probabilities, we derive optimality conditions. Additionally, we establish generalized convexity properties and stability conditions, which further underpin the robustness of our approach. This comprehensive framework finds significant applications in areas such as financial portfolio management and risk measure theory, where it provides powerful tools for addressing uncertainty, optimizing decision-making, and ensuring resilience against variability in probabilistic models.