Dynamic Portfolio Selection

In this chapter I recognize the importance of the stochastic programming as a significant tool in financial planning. The current practice of portfolio optimization is still limited to the simple formulation of linear programming (LR) or quadratic programming (QR) type. For that reason, relevant literature on asset-liability management (ALM) model has been reviewed and two different ALM approaches are compared: first piecewise linear function; and second a nonlinear utility function. This chapter shows that the mathematical programming methodology is ready to challenge the huge problem arising from LP portfolio optimization. A special emphasis was put on the shape of the investors' payoff functions in asset price equilibrium. The results underpin our claim that the nonlinear ALM model generated better asset allocation. An algorithmic construction of ALM model is developed in Wolfram Mathematica 9.

Extreme Events Theory and Application

In standard statistical methodologies, the probability that the extreme event will occur is very small. But the expected losses in real world markets are higher and sometimes with catastrophic outcomes. Here it seems that the fact that we could lose a certain amount of money 95% or 99% of the time tells us absolutely nothing about what could happen the other 5 or even 1 percent of the time. For that reason, instead of estimating the certain loss, as the standard statistical methodologies account, we introduce a technique known as a “tail risk protecting strategy” or “the barbell investment strategy.” In this chapter, analyzing the copper market movements I understand that the market has been conditioned to believe that the copper demand will exceed its supply. Therefore, I suggest to protect against a growing price-inflation risk. The analyses are conducted using the statistical software STATA 11 and Excel Spreadsheets.

Theory and Modelling

In this chapter, I discuss the dominance of the neoclassical theory. The effort here is to highlight the importance of studying economics as an adaptive complex system where the fractal structure and interaction play a fundamental explanatory role and individual details are largely relevant. To discard equilibrium in the standard sense and to move on to study out of equilibrium dynamics is surely the right way to proceed but is perhaps too big a step for economics at this time. Inspired of the Newton's model of the universe, economists developed an economic model that had the same formal properties. So, once economics and finance made it their goal to develop the concept and the idea of the elegant model form, they go along with the simplified assumptions of that form. Therefore, financial models can leave us unable to see many of the most important aspects of financial markets.

Portfolio Selection Models

The main goal behind the concept of portfolio management is to combine various assets into portfolios and then to manage those portfolios so as to achieve the desired investment objectives. To be more specific, the investors' needs are mostly defined in terms of profit and risk, and the portfolio manager makes a sound decision aimed ether to maximize the return or minimize the risk. The Mean-Variance and Mean-VaR analysis has gained widespread acceptance among practitioners of asset allocation. Although they are the simplest models of investment, sometimes they are sufficiently rich to be directly useful in applied problems and decision theory. Here you will learn how to apply these analyses in practice using computer programs and spreadsheets.

Decision Tree Analyses

As a branch of statistics that uses probability, decision trees have been widely applied to variety problems from numerous disciplines and serve two primary goals. First, they help us to resolve uncertainties in making investment decisions. Second, using decision trees we can determine which alternatives, at any point in time produces the most favorable, or least painful, consequences. In contrast, classical statistics focus on estimating a parameter, such as the population means, constructing a confidence interval, or conducting a hypothesis test. Classical statistics do not address the possible consequences of a decision. In this chapter I illustrate the essentials of using a decision tree for making financial decisions, and demonstrate how a decision is made using both criteria: expected monetary value and expected utility. At the end, I discuss the imperfectability of the traditional techniques and tools and suggest alternative decision tools inspired by some areas of research in signal processing, known as wavelet analysis. To set up and solve decision tree problems, TreePlan, and add-in for Excel, is used.

Fractal and Wavelet Market Analysis in Pattern Recognition

Fractal geometry can be seen as a universal language by which nature can be explained or at least described and quantified. Financial markets are one of them. Therefore, in this chapter, I set my focus on complex dynamics, an area that was around for about one hundred year ago and continues to inspire much ongoing research. I show that wavelet-based modelling underlies the process that generates financial market data. It is a method that decomposes a time series into several layers of time series, making it possible to analyze how the local variance, or wavelet power, changes both in the frequency and time domain. Then I calculate the local Holder exponent which is applied to estimate stable and unstable fixed point, or regularity and singularity and based on them, one can adapt its buy-sell strategy timely. The model successfully detects the hoarding effect, noise traders, and the pattern of the short-run price fluctuation. An algorithmic construction of the model is developed in Wolfram Mathematica 9 and MatLab R2016b.

Markov Processes in Finance With Application to Stock Markets

Important model that has evolved in the field of finance, is founded on the hypothesis of random walks and most often refers to a special category of Markov chain and Markov process. In these models the human race is presented as nothing more than a system with a large number of individual parts. If every human being acted totally independently of every other human being, then the human race as a whole would behave very much like a thermodynamic system. But people, in general, do not behave independently of each other. They have a tendency to cooperate and compete, which causes the human race to behave less like a thermodynamic system, and more like a complex adaptive system. The performed analysis in this chapter certifies the doubted that the discrete and continuous Markov processes as representations of stationary stochastic processes, cannot accurately anticipate the future trends.