This paper proposes a regression-based simulation algorithm for multi-period mean-variance portfolio optimization problems with constraints under a high-dimensional setting. For a high-dimensional portfolio, the least squares Monte Carlo algorithm for portfolio optimization can perform less satisfactorily with finite sample paths due to the estimation error from the ordinary least squares (OLS) in the regression steps. Our algorithm, which resolves this problem e, that demonstrates significant improvements in numerical performance for the case of finite sample path and high dimensionality. Specifically, we replace the OLS by the least absolute shrinkage and selection operator (lasso). Our major contribution is the proof of the asymptotic convergence of the novel lasso-based simulation in a recursive regression setting. Numerical experiments suggest that our algorithm achieves good stability in both low- and higher-dimensional cases.

中文翻译：

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基于套索的高维多期限投资组合仿真

针对高约束条件下具有约束条件的多周期均值-方差投资组合优化问题，提出了一种基于回归的仿真算法。对于高维投资组合，由于回归步骤中来自普通最小二乘（OLS）的估计误差，用于最小投资组合优化的最小二乘蒙特卡洛算法在有限样本路径下的性能可能无法令人满意。我们的算法解决了这个问题e，该算法证明了在有限样本路径和高维情况下数值性能的显着提高。具体来说，我们用最小绝对收缩和选择运算符（lasso）代替OLS。我们的主要贡献是在递归回归设置中基于新套索的模拟的渐近收敛的证明。