High-dimensional data analysis with constraints

Traditional Markowitz portfolio is very sensitive to errors in estimated input for a high dimensional dataset. This problem inspired us to connect the high dimensional portfolio selection problem to a constrained lasso problem to deal with the input uncertainty. In this paper, we developed a new alg...

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Main Author: Zhou, Hanxiao
Other Authors: Pun Chi Seng
Format: Final Year Project
Language:English
Published: Nanyang Technological University 2022
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Online Access:https://hdl.handle.net/10356/156929
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Institution: Nanyang Technological University
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spelling sg-ntu-dr.10356-1569292023-02-28T23:18:18Z High-dimensional data analysis with constraints Zhou, Hanxiao Pun Chi Seng School of Physical and Mathematical Sciences cspun@ntu.edu.sg Science::Mathematics Traditional Markowitz portfolio is very sensitive to errors in estimated input for a high dimensional dataset. This problem inspired us to connect the high dimensional portfolio selection problem to a constrained lasso problem to deal with the input uncertainty. In this paper, we developed a new algorithm using constrained lasso algorithm to solve the high dimension portfolio optimization problem. At the same time, the constrained lasso algorithm also could deal with the constraints of Aβ=C. However, because the selection of penalty factor relies on a noise σ in constrained lasso method, when it comes to high dimensional datasets, it will become very computational attractive. Thus, we studied scaled lasso and square root lasso on how they deal with the penalty level to the noise σ. Inspired by these two methods, we proposed two new algorithms which is constrained scaled lasso and constrained square-root lasso, which turns out effectively reduced the computational cost and works well in the high dimensional portfolio selection problem. We implemented the above mentioned algorithms and conduct an empire study to exam their performance and proved their capability in high dimensional portfolio selection problem. Bachelor of Science in Mathematical Sciences 2022-04-29T05:23:52Z 2022-04-29T05:23:52Z 2022 Final Year Project (FYP) Zhou, H. (2022). High-dimensional data analysis with constraints. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/156929 https://hdl.handle.net/10356/156929 en application/pdf Nanyang Technological University
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
spellingShingle Science::Mathematics
Zhou, Hanxiao
High-dimensional data analysis with constraints
description Traditional Markowitz portfolio is very sensitive to errors in estimated input for a high dimensional dataset. This problem inspired us to connect the high dimensional portfolio selection problem to a constrained lasso problem to deal with the input uncertainty. In this paper, we developed a new algorithm using constrained lasso algorithm to solve the high dimension portfolio optimization problem. At the same time, the constrained lasso algorithm also could deal with the constraints of Aβ=C. However, because the selection of penalty factor relies on a noise σ in constrained lasso method, when it comes to high dimensional datasets, it will become very computational attractive. Thus, we studied scaled lasso and square root lasso on how they deal with the penalty level to the noise σ. Inspired by these two methods, we proposed two new algorithms which is constrained scaled lasso and constrained square-root lasso, which turns out effectively reduced the computational cost and works well in the high dimensional portfolio selection problem. We implemented the above mentioned algorithms and conduct an empire study to exam their performance and proved their capability in high dimensional portfolio selection problem.
author2 Pun Chi Seng
author_facet Pun Chi Seng
Zhou, Hanxiao
format Final Year Project
author Zhou, Hanxiao
author_sort Zhou, Hanxiao
title High-dimensional data analysis with constraints
title_short High-dimensional data analysis with constraints
title_full High-dimensional data analysis with constraints
title_fullStr High-dimensional data analysis with constraints
title_full_unstemmed High-dimensional data analysis with constraints
title_sort high-dimensional data analysis with constraints
publisher Nanyang Technological University
publishDate 2022
url https://hdl.handle.net/10356/156929
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