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Mean-Variance Functional Estimation for Optimal Portfolios.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mean-Variance Functional Estimation for Optimal Portfolios./
作者:	Zhou, Yifeng.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	122 p.
附註:	Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
Contained By:	Dissertations Abstracts International82-12B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28497322
ISBN:	9798515271350

Mean-Variance Functional Estimation for Optimal Portfolios.
Zhou, Yifeng.

Mean-Variance Functional Estimation for Optimal Portfolios. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 122 p.

Source: Dissertations Abstracts International, Volume: 82-12, Section: B.

Thesis (Ph.D.)--Princeton University, 2021.

This item must not be sold to any third party vendors.

Motivated by Markowitz's portfolio optimization problem, this thesis aims at estimating functionals Σ −1 μ, μΣ −1 μ involving both the mean vector μ and covariance matrix Σ. These functionals are closely related to the optimal portfolio allocation and Sharpe ratio. The estimation problem is studied under the high-dimensional setting, and two different underlying structure are considered. In the first structure, sparsity of Σ −1 μ is assumed. Minimax estimators are obtained, and the optimal rate for estimating the functional μΣ −1 μ undergoes a phase transition between regular parametric rate and some form of high-dimensional estimation rate. It is further shown that the optimal rate is attained by a carefully designed plug-in estimator based on de-biasing, while a family of naive plug-in estimators are proved to fall short.The second structure is the approximate factor model. In this setting, we only assume finite fourth-moment. A robust procedure is proposed for estimating these functionals, and adaptive tuning is employed for implementation. These structures are well justified by empirical evidence, and they are suitable for practical implementation in different situation. Extensive numerical studies are presented which lend further support to the results.

ISBN: 9798515271350Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

Mean-variance

Mean-Variance Functional Estimation for Optimal Portfolios.
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500 $a Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
500 $a Advisor: Fan, Jianqing.
502 $a Thesis (Ph.D.)--Princeton University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Motivated by Markowitz's portfolio optimization problem, this thesis aims at estimating functionals Σ −1 μ, μΣ −1 μ involving both the mean vector μ and covariance matrix Σ. These functionals are closely related to the optimal portfolio allocation and Sharpe ratio. The estimation problem is studied under the high-dimensional setting, and two different underlying structure are considered. In the first structure, sparsity of Σ −1 μ is assumed. Minimax estimators are obtained, and the optimal rate for estimating the functional μΣ −1 μ undergoes a phase transition between regular parametric rate and some form of high-dimensional estimation rate. It is further shown that the optimal rate is attained by a carefully designed plug-in estimator based on de-biasing, while a family of naive plug-in estimators are proved to fall short.The second structure is the approximate factor model. In this setting, we only assume finite fourth-moment. A robust procedure is proposed for estimating these functionals, and adaptive tuning is employed for implementation. These structures are well justified by empirical evidence, and they are suitable for practical implementation in different situation. Extensive numerical studies are presented which lend further support to the results.
590 $a School code: 0181.
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650 4 $a Operations research. $3 547123
650 4 $a Finance. $3 542899
653 $a Mean-variance
653 $a Functional estimation
653 $a Optimal portfolios
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