Βελτιστοποίηση χαρτοφυλακίου μέσω ευρετικών τεχνικών προσομοίωσης
Porfolio optimization using heuristic simulation techniques
KeywordsΒελτιστοποίηση χαρτοφυλακίου ; Portfolio optimization ; Genetic algorithms ; Γενετικοί αλγόριθμοι ; Μεταευρετικοί αλγόριθμοι ; Metaheuristics
In this MSc thesis we study the key elements that determine the composition of a portfolio and highlight the advantages of diversification. Employing analytical methods and models that offer closed-form solutions we determine the optimal composition of an investment portfolio, either by minimizing a specific portfolio risk or by maximizing its expected utility. In a modern approach of the problem, Sharpe indicators combine both of these approaches. We also present some classical optimization methods such as quadratic programming, and we extensively analyze a new class of metaheuristic algorithms, which can deliver very good solutions in relatively fast computational time, offering excellent performance. In the first section we discuss in detail the most popular models of contemporary portfolio theory such as the Markowitz Model, the Black Model and the Tobin Model. Our review stems from the perspective of constrained optimization, and with the assistance of methods such as Lagrange multipliers and the Karush-Kuhn-Tucker conditions, we are able to derive closed-form solutions for the determination of the optimal composition of a financial portfolio. However, in cases where either the number or the type of constraints makes it impossible to find an analytical solution, we present in the next section appropriate numerical methods for approximating the optimal solution. In the second section we review the mechanisms of well known optimization algorithms, as well as some recently proposed metaheuristic algorithms and more specifically, Particle Swarm Optimization, Ant Colony Optimization and Random Search (Simulated annealing, Tabu search). In the third section, which consists of the main subject of our thesis, we present in detail an important class of metaheuristic algorithms, the so-called Genetic Algorithms. By employing the R programming language environment, their mechanisms and performance with respect to their parameters are numerically studied through specific examples, by presenting illustrating tables and graphs. Finally, in the fourth section, the genetic algorithms are applied to a specific case study related to the determination of the optimal composition of an investment portfolio based on historical values of returns on various investment securities.