Abstract

Asset allocation aims at constructing portfolios that follow a specific investment strategy, such as index tracking or optimal risk return. These strategies are formulated as optimization problems whose solutions represent an optimal portfolio depending on the strategy. In practice, these problems can be too complicated to be solved directly by deterministic optimization methods, which can lead to simplified models that may contain faulty assumptions or inaccuracies. When this is the case, metaheuristics such as Particle Swarm Optimization (PSO) may be needed. PSO is able to find optimal solutions to complex problems by evaluating random positions in the search space to iteratively approach the optimum. In this thesis, common asset allocation problems are first explained and solved using deterministic optimization methods to generate benchmark problems. After introducing the PSO, it is illustrated with simple examples and the convergence behavior is analyzed before it is subsequently tested on benchmark problems. Then, the PSO and its variants are used to solve optimization problems that cannot be solved by deterministic optimization methods. Finally, the most promising PSO variant is used to solve a discrete index tracking problem considering transaction costs and a rebalancing constraint. Backtests show that this PSO variant can provide time-stable results for such problems.