Wasserstein模糊下的多周期均值-期望投资组合优化：重构、退化与基础度量的作用

中文摘要 AI 辅助

期望损失（expectile）是唯一兼具一致性与可 elicitable 特性的法律不变风险度量。然而，与条件风险价值（CVaR）不同，期望损失不具备可实现易处理Wasserstein重构的Rockafellar-Uryasev表示。我们通过开发最坏情况期望损失的包络定理解决这一难题，该定理将Wasserstein模糊集上的最坏情况期望损失表征为具有分段仿射被积函数的最坏情况期望的唯一根。此表示允许直接应用标准Wasserstein对偶。利用该结果，我们将多周期三层均值-期望投资组合问题重构为四个带约束的参数线性规划。我们建立了所提模型的四个结构特性：内生阻尼的鲁棒性价格、决策依赖的临界半径（超过该半径后期望损失尾部分量不再起作用）、零模糊时名义模型的精确恢复，以及Wasserstein基础度量如何决定极限投资组合变得更集中或更分散的表征。对90个富时指数成分股在3341个样本外交易日的数值实验表明，在所有9个参数单元中，期望损失模型在模糊集、半径、基础度量和权衡权重匹配的情况下均优于CVaR模型，且当半径非平凡时优势显著。实验进一步证实了基础度量下的预测退化。

英文摘要

Expectiles are the only law-invariant risk measures that are both coherent and elicitable. Unlike Conditional Value-at-Risk (CVaR), however, they do not admit a Rockafellar--Uryasev representation that admits tractable Wasserstein reformulations. We address this difficulty by developing an envelope theorem for worst-case expectiles that characterizes the worst-case expectile over a Wasserstein ambiguity set as the unique root of a worst-case expectation with a two-piece affine integrand. This representation permits direct application of standard Wasserstein duality. Using this result, we reformulate a multi-period tri-level mean--expectile portfolio problem as four parametric linear programs with constraints. We establish four structural properties of the proposed model: an endogenously damped price of robustness, a decision-dependent critical radius beyond which the expectile tail component becomes inactive, exact recovery of the nominal model at zero ambiguity, and a characterization of how the Wasserstein ground metric determines whether the limiting portfolio becomes more concentrated or more diversified. Numerical experiments on 90 FTSE constituents over 3,341 out-of-sample trading days show that the expectile model outperforms a CVaR model matched on ambiguity set, radius, ground metric, and trade-off weight in all nine parameter cells---significantly so whenever the radius is non-trivial. The experiments further confirm the predicted degeneracy under the ground metric.

发表机构

• Indian Institute of Technology Delhi（印度德里理工学院）

机构由 AI 辅助整理，请以论文原文为准。