Burcu Adıgüzel Mercangöz - Applying Particle Swarm Optimization: New Solutions and Cases for Optimized Portfolios

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This book aims to provide theoretical and empirical research and application of portfolio optimization for the PSO technique. Therefore, it is hoped that this book provides the resources necessary for researchers, teachers, engineers, managers, and practitioners to adopt and implement the PSO technique in portfolio optimization with a comprehensive discussion on the issues.

The book focuses on one of the heuristic optimization techniques that proceeds from the inspiration of swarm intelligence: particle swarm optimization (PSO). The PSO is a very much popular swarm intelligence algorithm. It is a robust and well-researched optimization technique. It has its roots in artificial intelligence and animal communication strategy. It is one of the most preferred solution approaches in optimization problems due to its structure and advantages. Since its inception in the year 1995 by Eberhart and Kennedy, it is being applied to solve optimization problems in many domains, including portfolio optimization.

Optimization is the process of obtaining the best solution when performing certain operations for a given purpose. The problem of portfolio optimization is an important discipline of risk management in finance that consists in finding the optimum allocation among several assets. Constructing a highest return for a given portfolio of assets is a financial experts indisputable problem in which investors' interest is to construct a portfolio having a balance between the investors risk and their expectations about the portfolio returns. The general purpose of portfolio optimization is to discover an efficient frontier that yields the highest expected return on each level of portfolio risk. In reality, this problem usually deals with some constraints, such as the number of assets in a portfolio, transaction costs, and short sales. Solving this kind of problem is quite difficult because of the large amount of complex data and other constraints. In recent years, artificial intelligence techniques are mostly used in portfolio optimization. Before, optimization problems used to be defined by the mathematical functions. Due to the lack of flexibility and disadvantages of such methods, new methods have been developed and inspired by events in nature. Optimization algorithms based on natural events are called heuristic algorithms. Heuristic algorithms are the algorithms that are inspired by natural phenomena to accomplish any purpose or goal. There is a convergence to the optimum solution in the solution space, but no definite solution can be guaranteed in these algorithms. With the rise of the use of heuristics-based methods in problem solving, heuristics-based methods are widely used in quantitative decision making.

This book is structured into two parts. In the first part, the theoretical and mathematical background of portfolio construction and PSO method is mentioned and portfolio optimization cases solved by using the PSO method are given. The second part is about other application areas of PSO to give an idea and insight to the audience. Other than portfolio optimization, PSO applications in other fields such as renewable energies, operation and planning optimization, and image segmentation are included. The book totally contains 17 theoretical and empirical chapters. Chapters focus on different applications of PSO apart from portfolio optimization.

The details of the chapters are explained as below:

In the first chapter, titled Utility: Theories and model, the aim is to look at utility theory from a broad perspective. The main hypothesis in the theory of decision is that the person who is in the position of deciding is entitled to be called the economic man. Also, the individual acts rationally. Thus, utility is the ability to satisfy (eliminate) human needs of goods and services. Expected utility theory forms the basis of traditional finance. Expected utility theory assumes that people choose risky or uncertain opportunities by comparing the expected benefits from them. The Allais and Ellsberg paradoxes criticize expected utility theory. Kahneman and Tversky (1979) present that the expected utility axioms are violated for more reasonable lottery alternatives than in the Allais paradox and put a link between finance and psychology. The prospect theory of Kahneman and Tversky forms the basis of behavioral finance.

In the second chapter, titled Portfolio optimization, Markowitz's mean-variance model, which is the main model of modern portfolio theory, is explained and mathematical representations are given. The subject is supported with mathematical notations by mentioning concepts such as portfolio risk and return, efficient frontier, utility theory, asset allocation, indifference curves, Sharpe ratio, and coefficient of variation.