Sparse Portfolio

Sparse portfolio construction aims to create investment portfolios with a minimal number of assets while achieving desired performance goals, such as tracking a market index. Current research focuses on developing efficient algorithms, often employing $\ell_0$-norm constraints or topological data analysis coupled with clustering techniques, to select optimal asset combinations and manage portfolio sparsity directly. This approach offers benefits such as reduced transaction costs and mitigation of illiquidity risks, impacting both portfolio management practices and the development of more sophisticated optimization methods in finance.