A Dantzig-Type Large Portfolio Optimization Model and Its Efficient Fitting Algorithm
提出一种丹齐格型投资组合优化模型，通过引入惩罚项直接估计最优权重，支持多空头并满足和约束，结合资产分割的并行算法提升效率，在美股数据上验证了有效性。
Given the cyclical nature of market volatility and the increasing complexity of global financial systems, developing effective strategies for large-scale portfolio optimization is of critical importance. In this work, we propose a novel Dantzig-type portfolio optimization (DPO) model designed to help investors navigate these challenges and optimize their portfolios effectively. The model separately incorporates ℓ1 and folded concave penalties, enabling the direct estimation of optimal portfolio weights while enforcing the sum constraint and accommodating both long and short positions. We establish the desired theoretical properties under mild regularity conditions, and introduce efficient parallel computing algorithms based on asset-splitting. Through extensive simulation studies, we investigate the superior effectiveness and efficiency of the DPO model and proposed algorithms. Furthermore, we illustrate the usefulness of the model by applying it to U.S. stock market datasets, including the constituent stocks of both S&P 500 and Russell 2000 indices.