Development of optimization algorithms for asset allocation in multicomponent investment portfolios

Abstract

This article is devoted to the development and research of optimization algorithms for solving the problem of asset allocation in multicomponent investment portfolios, which is one of the key problems in the theory of finance. More generally, the task is to find a capital allocation between different assets that minimizes risks and maximizes expected returns, which requires the effective use of mathematical optimization methods. The Introduction describes the basic concepts of building investment portfolios, provides general information about classical approaches such as Markowitz portfolio theory, and highlights the main problems associated with computational complexity with a high number of assets. Further, the article argues for the need to develop new or modified algorithms to improve the efficiency of asset allocation in a multicomponent environment. The methodological part (Methods) presents optimization algorithms, including stochastic and deterministic methods that are applied to this task. The main techniques used, such as genetic algorithms, Lagrange methods, and the simplex method, are described. This section also examines the constraints imposed on the models (for example, limits on the minimum and maximum share of assets), as well as other practical aspects such as market liquidity and transaction costs. The Results show that using the proposed algorithms leads to more balanced portfolios with improved profitability characteristics compared to traditional methods. Then a comparative analysis is carried out between the various proposed solutions. The conclusion highlights the importance of further research in this area and suggests possible directions for future work, including the integration of machine learning algorithms to improve methods for predicting asset returns.