C61 - Optimization Techniques; Programming Models; Dynamic AnalysisReturn

Two levels can be identified in the article. The first one is related to a theoretical introduction to the known stochastic dominance approach and the interactive multi-objective programming method; in the second we apply the aforesaid quantitative approaches to making an "optimal" portfolio structure of shares funds. We use the draft of stochastic dominance for a reduction in a relatively huge set of investment opportunities. The application of the stochastic dominance principle is determined by the stochastic character of the studied problem. The yield rate of shares funds is stated as a random variable. We also apply the Monte Carlo method in the investment decision-making procedure. For finding an "optimal" portfolio form, we use the interactive multi-criteria programming method, the computational algorithm of which is based on maximization of positive deviation from aspiration levels of separate objective functions (criteria). After all the procedures, including successive revision of solutions offered by analysts according to decision-maker preferences, we obtain a final portfolio form of shares funds.

The paper deals with two methods of solving optimization programs where uncertainties occur: stochastic (in particular chance-constrained) programming and robust programming. We review briefly how these two methods deal with uncertainty and what approximations are commonly used. Furthermore, we are concentrated on approximations based on sample sets where some type of weak dependence occurs. We demonstrate that such kind of dependence does not imply any important malfunction of optimization methods used there. Numerical illustration on simple optimization program is given.

In this note, we consider in discrete time the Ramsey growth model without discounting under stochastic uncertainty modelled by Markov processes. To make the model computationally tractable we shall consider finite state approximations of the original model. Properties of policies maximizing mean value of the global utility of consumers over an infinite time horizon, along with algorithmic procedures finding optimal and suboptimal policies, are reported.

The paper is concerned with an implementation of behavioral aspects of a heterogeneous agents model (HAM) with the worst out algorithm (WOA). The WOA replaces periodically the trading strategies that have the lowest performance level of all strategies presented on the market by the new ones. The model includes a possibility to change the mood of the investors on the market. This modification allows for changing phases of optimism and pessimism. This feature enables generation of more realistic financial time series. It is shown how a mood change on the financial market influence a persistence of financial time series.

The article presents and investigates new possibilities of multivariate data visualization and their analytical convenience. We demonstrate elementary principles, algorithms and graphical outputs of modern visualization methods with particular focus on Bertin matrices, RADVIZ, Projection pursuit and parallel coordinates. Illustrative examples show their practical implementation into the process of multivariate data analysis, hence providing the reader with an idea of the wide range of their application.