High-dimensional data analysis with constraints - Zhou, Hanxiao (Nanyang Technological University, 2022)
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.