依赖不确定性下的投资组合分散化与集中化：一种优化方法
Portfolio Diversification and Concentration under Dependence Uncertainty: A Majorization Approach
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中文总结 AI 辅助
本文针对依赖不确定性下的投资组合优化问题，基于优化序框架推导了多种风险测度的最坏情况不等式，发现了“集中悖论”并提出加权稳健性公式，为平衡分散化与稳健性提供了理论支撑。
中文摘要 AI 辅助
现代投资组合理论将分散化视为降低风险的主要工具，但在模型不确定性下，这一基石可能不再最优。本文研究依赖不确定性下投资组合分散化与集中化之间的权衡关系。在无模型不确定性时，我们采用优化序（majorization order）和双随机矩阵框架来形式化分散化程度，证明拟凸性是风险泛函与优化序弱一致的充要条件。我们进一步推导了针对包括VaR、ES、区间VaR（RVaR）和标准差（SD）在内的广泛风险测度的最坏情况风险测度不等式，并求解了稳健投资组合选择问题。我们的结果揭示了许多常用风险泛函的“集中悖论”：当依赖结构完全不确定时，稳健优化常建议将投资集中于单一资产以对冲最坏情况依赖场景。作为应用，我们提出了一种加权稳健性公式，该公式在参考依赖结构与最坏情况结构之间进行插值，其结构与《交易对手资本规则》（FRTB）中受约束/无约束预期短缺的组合类似，为存在模型不确定性时平衡分散化与稳健性提供了理论基础。
英文摘要
Modern portfolio theory identifies diversification as the primary tool for risk reduction. However, under model uncertainty, this cornerstone may no longer remain optimal. This paper investigates the tension between portfolio diversification and concentration under dependence uncertainty. In the absence of model uncertainty, we employ the framework of the majorization order and doubly stochastic matrices to formalize the degree of diversification, and prove that quasi-convexity is a necessary and sufficient property for a risk functional to be weakly consistent with the majorization order. We further derive worst-case risk measure inequalities and solve robust portfolio selection problems for a broad class of risk measures, including VaR, ES, Range-VaR (RVaR), and standard deviation (SD). Our results reveal a ''concentration paradox'' for many widely-used risk functionals: when the dependence structure is fully ambiguous, robust optimization often recommends concentrating investment in a single asset to hedge against the worst-case dependence scenario. As an application, we propose a weighted robustness formulation that interpolates between a reference dependence structure and the worst-case structure. The formulation is structurally analogous to the constrained/unconstrained Expected Shortfall blend in the Fundamental Review of the Trading Book (FRTB) and provides a theoretical foundation for balancing diversification against robustness in the presence of model uncertainty.
发表机构
- University of Essex（埃塞克斯大学）
- The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））
机构由 AI 辅助整理，请以论文原文为准。
