多元正态均值-方差混合中的混合律不确定性：半参数估计与稳健累积前景决策
Mixing-Law Uncertainty in Multivariate Normal Mean-Variance Mixtures: Semi-parametric Estimation and Robust Cumulative-Prospect Decisions
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中文总结 AI 辅助
研究多元正态均值-方差混合中混合律不确定性，通过比较六种参数混合律与非参数估计器确定有限模糊集，考虑累积前景问题，证明相关结果并应用于股票回报，表明混合模型表现优，最坏情况模型在投资组合优化阶段确定。
中文摘要 AI 辅助
正态均值-方差混合的分布取决于其正混合变量的定律。我们在相同的行列式识别约束下，将六种参数混合律与网格非参数最大似然估计器进行比较。估计混合均值\(m = \E(Z)\)且不固定为1。使用配对块自举法比较多元留出对数分数。无法与得分最高的模型区分开的模型定义了一个有限模糊集。然后我们考虑一个关于共同投资组合方向的累积前景问题。对于集合中的每个模型，NMVM表示给出一个标量投影回报和相应的风险敞口前景价值函数。分布稳健决策使这些函数的下包络最大化。我们证明了解的存在性，给出了分段光滑问题候选点，推导了参考差距缩放结果，并为有限场景最优构建了区间分支定界证书。在对30只股票回报的应用中，混合模型比多元高斯模型给出更高的留出密度分数。然而，几个参数和半参数模型仍在模糊集中。因此，最坏情况模型是在投资组合优化阶段确定的，而不是从留出分数的点估计中预先选择。
英文摘要
The distribution of a normal mean-variance mixture depends on the law of its positive mixing variable. We compare six parametric mixing laws with a grid nonparametric maximum likelihood estimator under the same determinant identification constraint. The mixing mean $m=\E(Z)$ is estimated and is not fixed at one. A paired block bootstrap is used to compare multivariate holdout log scores. The models that cannot be distinguished from the model with the largest score define a finite ambiguity set. We then consider a cumulative prospect problem on a common portfolio direction. For each model in the set, the NMVM representation gives a scalar projected return and a corresponding prospect-value function of the exposure. The distributionally robust decision maximizes the lower envelope of these functions. We prove existence of a solution, give the candidate points for the piecewise smooth problem, derive a reference-gap scaling result, and construct an interval branch-and-bound certificate for the finite-scenario optimum. In an application to 30 stock returns, the mixture models give higher holdout density scores than the multivariate Gaussian model. Several parametric and semi-parametric models, however, remain in the ambiguity set. The worst-case model is therefore determined at the portfolio optimization stage rather than selected in advance from a point estimate of the holdout score.
