A Novel Dynamic Neural System for Nonconvex Portfolio Optimization With Cardinality Restrictions
Xinwei Cao, Shuai Li
Abstract
The Markowitz model, a portfolio analysis model that won the Nobel Prize, lays the theoretical groundwork for modern finance. The transaction cost and the cardinality restriction, which were not covered in Markowitz model, are becoming increasingly important with the advent of high-frequency trading era. However, it remains a challenging problem to consider those constraints due to the nonconvex nature of the problem. A novel dynamic neural network, inspired by its successes in machine learning, is developed to tackle this difficult issue. Theoretical analysis is provided for the convergence of the designed neural network. Experimental results using real stock market data confirm the effectiveness of the proposed model. With the proposed model, the cost function characterizing the overall risks, and rewards is reduced by 123.6% from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-4.549\times 10^{-5}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-1.0173\times 10^{-4}$ </tex-math></inline-formula> . This indicates that the proposed strategy is successful in reducing risks and increasing rewards.