ONLINE ROBUST PORTFOLIO RISK MANAGEMENT USING TOTAL LEAST-SQUARES AND PARALLEL SPLITTING ALGORITHMS

The present paper introduces a novel online asset allocation strategy which accounts for the sensitivity of Markowitz-inspired portfolios to low-quality estimates of the mean and the correlation matrix of stock returns. The proposed methodology builds upon the total least-squares (TLS) criterion regularized with sparsity attributes, and the ability to incorporate additional convex constraints on the portfolio vector. To solve such an optimization task, the present paper draws from the rich family of splitting algorithms to construct a novel on-line splitting algorithm with computational complexity that scales linearly with the number of unknowns. Real-world financial data are utilized to demonstrate the potential of the proposed technique. Index Terms — Markowitz portfolio, total least-squares, spar-sity, splitting algorithms, proximal mapping, projection