الگوریتم های تکاملی چندمنظوره برای مدیریت پرتفولیو : مروری بر مقالات جامع

In this paper we provide a review of the current state of research on Portfolio Management with the support of Multiobjective Evolutionary Algorithms (MOEAs). Second we present a methodological framework for conducting a comprehensive literature review on the Multiobjective Evolutionary Algorithms (MOEAs) for the Portfolio Management. Third, we use this framework to gain an understanding of the current state of the MOEAs for the Portfolio Management research field and fourth, based on the literature review, we identify areas of concern with regard to MOEAs for the Portfolio Management research field.

Multiobjective optimization (MO) is the problem of simultaneously optimizing two or more conflicting objectives subject to certain constraints. Many real-world problems involve simultaneous optimization of several often conflicting objectives. The portfolio optimization problem is a characteristic example of this category of problems. According to Markowitz’s (1952) mean–variance theory (MV) an investor attempts to maximize portfolio expected return for a given amount of portfolio risk or minimize portfolio risk for a given level of expected return. The MV theory was criticized for unrealistic assumptions. Responding to the critics, researchers incorporated to the portfolio model some real world constraints like bounds on holdings, cardinality, minimum transaction lots and sector capitalization constraints. Moreover they proposed new risk measures such as the value-at-risk (VaR), the lower partial moments (LPM) of nth order, the conditional value-at-risk (CVaR) ( kibzun & Kuznetsov, 2006), and the conditional drawdown-at-risk (CDaR) ( Balzer, 1994). However, these additional constraints and risk measures made the Portfolio Selection problem difficult to be solved with exact methods. Evolutionary algorithms (EAs) have become the method of choice for optimization problems that are too complex to be solved using deterministic techniques. EAs are well suited to multiobjective optimization problems (MOP) as they are inspired by the biological processes which are inherently multiobjective. Thanks to Multiobjective Evolutionary Algorithms (MOEAs) techniques the classical portfolio model can be extended to handle two or more conflicting objectives subject to various realistic constraints. Because the various objectives functions in the portfolio selection problem are usually in conflict with each other, each time that we attempt to optimize further an objective other objectives suffer as a result. Therefore, the objective in MOEAs is to find the Pareto front of efficient solutions that provide a tradeoff between the various objectives. During the last decade MOEAs for the Portfolio Management have attracted attention from both academics and practitioners and we feel that now is a good time to study how the MOEAs for the Portfolio Management field has evolved and what its present state is. The purpose of this paper is fourfold. The first objective is to present the current state of research in Portfolio Management with the support of MOEAs by providing a brief review of the available literature in the field. The second objective is to develop a methodological framework for conducting a comprehensive literature study based on the papers published in MOEAs for the Portfolio Management over a long time span across various disciplines. The third objective is to use this framework to gain an understanding of the current state of the MOEAs for the Portfolio Management research field. The fourth objective is, based on the literature review, to identify potential areas of concern in regard to MOEAs for the Portfolio Management. The paper is organized as follows. In Section 2 we present the most well known techniques for multiobjective optimization with the use of MOEAs. In Section 3 we provide a brief review of the available literature in Portfolio Management with the support of MOEAs. In Section 4 the methodological framework for carrying out the literature study is presented and additionally the findings of the review are analyzed. Finally, in Section 5 we identify some possible paths for future research in MOEAs for the Portfolio Management.

The purpose of this report is to provide an insight into the current state of research in Multi-objective Evolutionary Algorithms focusing on the Portfolio Management. To serve this purpose we analyzed 91 papers according to journal, author and nationality of authors’ institution. Moreover we addressed issues related to the problem’s formulation such as which are the most popular objectives, constraints and risk measures applied in the Portfolio Management models with the support of MOEAs. On top of that we presented the various disciplines and the research methodologies of the available literature in the field. We started by presenting the methodological framework for the analysis of the available literature on the Multi-objective Evolutionary Algorithms focusing on the Portfolio Management. Then we presented graphically the sharp increase in the number of papers published in MOEAs field independent, to name some of them: engineering, science, finance, biology, medicine, genetics, robotics, physics and chemistry over the period 1994–2011. For the same period of time we presented the number of papers published in MOEAs focusing on the Portfolio Management and we noticed a relatively small increase compared with the impressive increase in the volume of papers published in MOEAs as a total. This indicates clearly that the undergoing research for the implementation of MOEAs to the Portfolio Selection problem is in its early stages and there is a lot of room for further research. Furthermore, our analysis revealed that almost 80% of the authors in Portfolio Management with the support of MOEAs have contributed a single paper and only 14.57% have contributed to two papers. Moreover we found out that US, UK and German institutions have contributed the most to the study of the MOEAs focusing on Portfolio Management. Chinese and Indian institutions are next with about 6.7% of the total publications produced to each one of these two countries. Significant contribution to the study of the field display institutions of smaller countries like Austria, Greece, Ireland and Switzerland. The analysis revealed that 82.50% of the MOEAs for Portfolio Management models make use of only two objectives and that the portfolio’s expected return and variance are the most popular among them, followed by VaR, Annual Dividends, Expected Shortfall and Skewness. Moreover we found that the most widely used risk measure in the relevant literature is the Variance, followed by VaR, Expected Shortfall and Skewness. Another issue of concern in our study was how many constraints are used by the authors in the formulation of MOEAs for Portfolio Management models. We found that the majority of the scholars used two constraints. Additionally we found that the most widely used constraints are the Cardinality constraints followed by the Lower and Upper bounds, Transaction Roundlots and Sector or Class capitalization constraints. The next question we had to answer was which disciplines have contributed the most to the development of MOEAs focusing on the Portfolio Management. We found out that the two dominant disciplines are those of Operations Research and Computer Science. A final issue of concern in our analysis was to identify the methodological classification of choice for the authors of papers in MOEAs for the Portfolio Management. About 81.31% of the authors chose the Combined methodological approach, and a huge majority, about 95.95% of the authors who chose the Combined methodological approach selected a combination of Model design and Empirical – Experiment methodological approach.