ℓ 2 -Relaxation: With Applications to Forecast Combination and Portfolio Analysis
提出一种新的凸优化方法ℓ2-松弛，用于处理高维预测组合或最小方差投资组合问题，通过最小化权重向量的欧几里得范数并加入松弛线性不等式来平衡偏差与方差，在潜在块等相关模式下实现近似等权分组最优。
Abstract We propose ℓ2-relaxation, which is a novel convex optimization problem, to tackle a forecast combination with many forecasts or a minimum variance portfolio with many assets. ℓ2-relaxation minimizes the squared Euclidean norm of the weight vector subject to a set of relaxed linear inequalities to balance the bias and variance. It delivers optimality with approximately equal within-group weights when latent block equicorrelation patterns dominate the high-dimensional sample variance-covariance matrix of the individual forecast errors or the assets. Its wide applicability is highlighted in three real data examples in microeconomics, macroeconomics, and finance.