An Evolutionary Approach to Multistage Portfolio Optimization

Portfolio optimization is an important problem in quantitative finance due to its application in asset management and corporate financial decision making. This involves quantitatively selecting the optimal portfolio for an investor given their asset return distribution assumptions, investment objectives and constraints. Analytical portfolio optimization methods suffer from limitations in terms of the problem specification and modelling assumptions that can be used. Therefore, a heuristic approach is taken where Monte Carlo simulations generate the investment scenarios and' a problem specific evolutionary algorithm is used to find the optimal portfolio asset allocations. Asset allocation is known to be the most important determinant of a portfolio's investment performance and also affects its risk/return characteristics. The inclusion of equity options in an equity portfolio should enable an investor to improve their efficient frontier due to options having a nonlinear payoff. Therefore, a research area of significant importance to equity investors, in which little research has been carried out, is the optimal asset allocation in equity options for an equity investor. A purpose of my thesis is to carry out an original analysis of the impact of allowing the purchase of put options and/or sale of call options for an equity investor. An investigation is also carried out into the effect ofchanging the investor's risk measure on the optimal asset allocation. A dynamic investment strategy obtained through multistage portfolio optimization has the potential to result in a superior investment strategy to that obtained from a single period portfolio optimization. Therefore, a novel analysis of the degree of the benefits of a dynamic investment strategy for an equity portfolio is performed. In particular, the ability of a dynamic investment strategy to mimic the effects ofthe inclusion ofequity options in an equity portfolio is investigated. The portfolio optimization problem is solved using evolutionary algorithms, due to their ability incorporate methods from a wide range of heuristic algorithms. Initially, it is shown how the problem specific parts ofmy evolutionary algorithm have been designed to solve my original portfolio optimization problem. Due to developments in evolutionary algorithms and the variety of design structures possible, a purpose of my thesis is to investigate the suitability of alternative algorithm design structures. A comparison is made of the performance of two existing algorithms, firstly the single objective stepping stone island model, where each island represents a different risk aversion parameter, and secondly the multi-objective Non-Dominated Sorting Genetic Algorithm2. Innovative hybrids of these algorithms which also incorporate features from multi-objective evolutionary algorithms, multiple population models and local search heuristics are then proposed. . A novel way is developed for solving the portfolio optimization by dividing my problem solution into two parts and then applying a multi-objective cooperative coevolution evolutionary algorithm. The first solution part consists of the asset allocation weights within the equity portfolio while the second solution part consists 'ofthe asset allocation weights within the equity options and the asset allocation weights between the different asset classes. An original portfolio optimization multiobjective evolutionary algorithm that uses an island model to represent different risk measures is also proposed.Imperial Users onl

A specialized island model and its application in multiobjective optimization

Abstract. This paper discusses a new model of parallel evolutionary algorithms (EAs) called the specialized island model (SIM) that can be used to generate a set of diverse non-dominated solutions to multiobjective optimization problems. This model is derived from the island model, in which an EA is divided into several subEAs that exchange individuals among them. In SIM, each subEA is responsible (i.e., specialized) for optimizing a subset of the objective functions in the original problem. The efficacy of SIM is demonstrated using a three-objective optimization problem. Seven scenarios of the model with a different number of subEAs, communication topology, and specialization are tested, and their results are compared. The results suggest that SIM effectively finds non-dominated solutions to multiobjective optimization problems.