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Creation of equity portfolio under unusual market conditions by using the methods of decision making
Čižmař, Adam ; Borovička, Adam (advisor) ; Sokol, Ondřej (referee)
This bachelor thesis deals with problems of investing in stock market. There are plenty of different approaches to investing into stocks, however methods used in this thesis belong among multi-criteria decision making methods. Such an aproach is not commonly used which provides an interesting point of view that differs from widely used methods. This thesis consists of theoretical background to market environment and stocks themselves and also of theoretical description of multi-criteria evaluation and multi-criteria programming. Specifically I use ELECTRE I method as multi-criteria evaluation and aggregation of linear functions as multi-criteria programming method. By using these two methods I create two different portfolios based on two separate strategies. First of them aims to maximize capital gains whereas the second one aims to maximize dividend profits and to minimize risk, as well.
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Econometric analysis of unemployment in Czech republic
Melnyk, Anastasiia ; Formánek, Tomáš (advisor) ; Sokol, Ondřej (referee)
This bachelor thesis deals with the issue of unemployment in general, and in the practical part concretely - unemployment rate in the Czech Republic and Austria. Firstly, the thesis examines the theory of general concepts for getting acquainted with unemployment in an open economy, then explains different types of unemployment and the factors that cause them. Separately describes Okun's law and introduces the regression equation, which will be verified later on empirical data. Next, it will introduce to us selected econometric methods of unemployment analysis, primarily focusing on the problems of time series, with which it will work in the practical part. Particularly, it will describe general terms in econometrics, techniques of estimation of parameters for regression equation, decomposition of time series and their characteristics, use of dummy variables in econometric modeling, econometric and statistical verification of model. In the practical part empirical analysis and evaluation of the results are going to be performed - firstly, decomposition of time series and proper seasonal adjustment.,then test of time series for unit root and subsequently differentiation for detrending. As a hypothesis, some of the factors described in the theoretical part will be selected:: citizens' level of education, minimum wage, global crisis of 2008, intervention of CNB, and GDP (based on Okun's law). Regression of unemployment rate on individual factors will be run, the model also will be gradually expanded by other variables and will be tested for the unit root and heteroskedasticity. Estimates using the Generalized Least Squares method will be compared to the OLS estimates. Thesis will be summarized by conclusion of the empirical analysis.
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Transportation theory in practice
Sojka, Jiří ; Dlouhá, Zuzana (advisor) ; Sokol, Ondřej (referee)
One of the most widely used optimization problems is vehicle routing problem. With minor adjustments of the limiting constraints it is usable on large variety of problems in fields of logistics or delivery of goods. The goal is to help company Víno Hruška s.r.o. to find a route for distribution of advertising materials to their own branches in the Czech Republic and Slovakia. First part is dedicated to theoretical introduction to methods of linear programming, second part is practical and uses described methods with real data. Routes found with heuristic methods and with optimization software are compared.
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Stability measures of optimal solution of LP problems with regards to the target function
Sůra, Jan ; Pelikán, Jan (advisor) ; Sokol, Ondřej (referee)
Real-world systems usually contain some degree of natural uncertainty, their parameters are more or less variable. When seeking optimal solution, optimization models often disregard this variability and consider parameters of the model to be constant. This thesis focuses on methods of post-optimization analysis. Thorough post-optimization analysis should be a part of every optimization process of systems with variable parameters. Post-optimization analysis can identify parameters whose variability poses the greatest threat to the systems performance. This thesis describes some of the basic post-optimization methods and then a new method based on interval arithmetics is formulated.
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Long steps in IPM and L_1-regression
Šicková, Barbora ; Černý, Michal (advisor) ; Sokol, Ondřej (referee)
This work deals with Newton method of interior point which is applied on finding estimation of polynomial L_1 regression. The aim of this thesis is to find new modifications of long step choice in Newton method in order to find faster solution of L_1 estimations for large data sets. Designed modifications are based on full-Newton step algorithm for the self-dual model. According to reasults, the best are algorithms AF-L, F-LP1, AF-LP1 a AF-L-mixed, which modify the barrier update parameter in adaptive way. Algorithms and obtained results were implemented end visualized in MatLab.
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Interval data and sample variance: computational aspects
Sokol, Ondřej ; Černý, Michal (advisor) ; Rada, Miroslav (referee)
This thesis deals with the calculation of the upper limit of the sample variance when the exact data are not known but intervals which certainly contain them are available. Generally, finding the upper limit of the sample variance knowing only interval data is an NP-hard problem, but under certain conditions imposed on the input data an appropriate efficient algorithm can be used. In this work algorithms were modified so that, even at the cost of exponential complexity, one can always find the optimal solution. The goal of this thesis is to compare selected algorithms for calculating the upper limit of sample variance over interval data from the perspective of the average computational complexity on the generated data. Using simulations it is shown that if the data meets certain conditions, the complexity of the average case is polynomial.
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