Advances in Portfolio Selection Under Discrete Choice Constraints: A Mixed-integer Programming Approach and Heuristics

Over the last year or so, we have witnessed the global effects and repercussions related to the field of finance. Supposed blue chip stocks and well-established companies have folded and filed for bankruptcy, an event that might have thought to been absurd two years ago. In addition, finance and investment science has grown over the past few decades to include a plethora of investment options and regulations. Now more than ever, developments in the field are carefully examined and researched by potential investors. This thesis involves an investigation and quantitative analysis of key money management problems. The primary area of interest is Portfolio Selection, where we develop advanced financial models that are designed for investment problems of the 21st century. Portfolio selection is the process involved in making large investment decisions to generate a collection of assets. Over the years the selection process has evolved dramatically. Current portfolio problems involve a complex, yet realistic set of managing constraints that are coupled to general historic risk and return models. We identify three well-known portfolio problems and add an array of practical managing constraints that form three different types of Mixed-Integer Programs. The product is advanced mathematical models related to risk-return portfolios, index tracking portfolios, and an integrated stock-bond portfolio selection model. The numerous sources of uncertainty are captured in a Stochastic Programming framework, and Goal Programming techniques are used to facilitate various portfolio goals. The designs require the consideration of modelling elements and variables with respect to problem solvability. We minimize trade-offs in modelling and solvability issues found in the literature by developing problem specific algorithms. The algorithms are tailored to each portfolio design and involve decompositions and heuristics that improve solution speed and quality. The result is the generation of portfolios that have intriguing financial outcomes and perform well with respect to the market. Portfolio selection is as dynamic and complex as the recent economic situation. In this thesis we present and further develop the mathematical concepts related to portfolio construction. We investigate the key financial problems mentioned above, and through quantitative financial modelling and computational implementations we introduce current approaches and advancements in field of Portfolio Optimization.Ph