Swarm Intelligence Algorithms for Portfolio Optimization Problems: Overview and Recent Advances

Abstract

Due to the volatility and uncertainty of the financial market, investors often use the form of portfolio to actively manage their assets. Portfolio optimization (PO) is becoming more and more important for investors. However, PO is frequently a kind of NP-hard problem in the field of modern financial optimization, which has gradually attracted the attention and interest of researchers. Some efficient mathematical models were built to describe the return and risk of portfolio. A lot of precise and approximate fast algorithms are used to solve the established PO models. The fundamental purpose is to maximize the return and to minimize the risk of portfolio under certain constraints. In recent years, researchers not only limit the goal of PO to the balance between risk and return, but also pay attention to liquidity, environmental, social, and governance (ESG) controversy level, Sortino ratio, and other indicators. The number of PO targets and constraints is further extended. In the past two decades, swarm intelligence (SI) algorithms have been widely introduced to solve PO problems. SI algorithm is mainly inspired from the daily phenomena in nature or self-organization, self-adaptation, and self-learning of biological population. The existing research results show that SI algorithm has the characteristics of high efficiency and can obtain satisfactory solutions in solving PO problems. The recent advances on the classic portfolio optimization concepts, models, and the usual SI-based solving algorithms are presented. Finally, future potential research directions are presented.

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“…Maximum order is reflected by Shannon holes, which produce zero structural information for perfect structures [1], an observation we have attributed first to Shannon. For intelligent humans in opposition to a non-perfect structure, that accounts for why probes are necessary to find vulnerabilities in an opponent's structure; 12 why deception seeks to reduce the disorder created by a spy's presence works well in intelligence, 13 combat, business and science (after confirmation of the perihelion motion of Mercury, Einstein was not immediately forthcoming with his competitor Hilbert until Hilbert assured him that his discovery was safely his alone); and why knowledge, especially its structure, is not only difficult to improve upon, but that its function is successful and generalizable (viz., Einstein's general theory of relativity).…”