On the role of norm constraints in portfolio selection
On the role of norm constraints in portfolio selection
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DOI：
10.1007/s10287-011-0130-2
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发表时间：
2011-08
影响因子：
0.9
通讯作者：
Jun-ya Gotoh;A. Takeda
中科院分区：
文献类型：
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作者：
Jun-ya Gotoh;A. Takeda
为了减小最优投资组合中的估计误差，已经提出了几种投资组合选择的优化方法。其中包括范数约束方差最小化和鲁棒投资组合模型。在本文中，我们从几个方向研究了范数约束在投资组合优化中的作用。首先，它表明，范数约束可以被视为一个强大的约束与返回向量。第二，风险价值（VaR）和条件风险价值（CVaR）最小化的鲁棒对应物的重新表达包含范数项，并且被证明与ν-支持向量机（ν-SVM）高度相关，ν-SVM是一种强大的统计学习方法。对于范数约束的VaR和CVaR最小化，基于ν-SVM的推广误差界，给出了非参数的理论验证.第三，将范数约束方法应用于跟踪投资组合问题。计算实验表明，范数约束最小化与参数调整策略改善了传统的范数无约束模型的样本外跟踪误差。
Several optimization approaches for portfolio selection have been proposed in order to alleviate the estimation error in the optimal portfolio. Among them are the norm-constrained variance minimization and the robust portfolio models. In this paper, we examine the role of the norm constraint in portfolio optimization from several directions. First, it is shown that the norm constraint can be regarded as a robust constraint associated with the return vector. Second, the reformulations of the robust counterparts of the value-at-risk (VaR) and conditional value-at-risk (CVaR) minimizations contain norm terms and are shown to be highly related to theν-support vector machine (ν-SVM), a powerful statistical learning method. For the norm-constrained VaR and CVaR minimizations, a nonparametric theoretical validation is posed on the basis of the generalization error bound for theν-SVM. Third, the norm-constrained approaches are applied to the tracking portfolio problem. Computational experiments reveal that the norm-constrained minimization with a parameter tuning strategy improves on the traditional norm-unconstrained models in terms of the out-of-sample tracking error.