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Optimization methods in finance
Baník, Peter ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In this diploma paper we discuss selected optimization methods and mathematical programming models. We focus on optimization models of optimal portfolio selection problem. We consider the problem of finding optimal portfolio under criterion of maximizing expected return and risk minimizing. For selected risk measures we use convenient mathematical models. There are adequate optimization techniques for problems of linear and quadratic programming. For general nonlinear problems we use advanced stochastic optimization algorithms. We numerically illustrate the methods on real data examples using the Mathematica software. Presented results give comparisons both for models and methods. We also focus on computational complexity of optimization algorithms and study the influence of input parameters on the results.
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Stochastic models for genetic analysis
Selementová, Martina ; Kulich, Michal (advisor) ; Zichová, Jitka (referee)
Nazev prace: Slochasticke niodcly pro geneliekou analyzu Autor: MartinaSelementova Katedra: Katedra pravdepodobnosti a matematicke statistiky Vedouci bakalafske prace: Mgr. Michal Kulich, PhD, e-mail vedouciho: kuliclX^karlin.mff.cuni.cz Abstrakt: V pfedlozene praci studujerne elementarni stochasticke melody pro modelovani genetickych populaci. Nejprve uvadime zakladni pojmy obecne gcnetiky pro snadnejsi oricntaci v textu. V naslcdujicich kapitolach se zabyvame dynamikou vyvoje populace a zakladnimi problemy vyberu v populaci. lllavnim tcmatem je nahodne kfizeni v populaci, ktcre dale aplikujeme na pohlavne va/ane geny, letraploidy. autosterilizacni geny a na pfi'pad dvou lokusu. Ve druhe casti se xabyvame problemy vybcru: zamC'fili jsme se pf-edevsim na vyber xalozeny na gcnolypu aplikovany na pohlavi a pohlavne vazane geny a dale na lamiliarni vyber a konkretnf pn'klad Rh faktoru. Klicova slova: nahodne kfizeni, vyber Title: Stochastic Models for Genetic Analysis Author: Martina Selementova Department: Department oi'Probability and Mathematical Statistics Supervisor: Mgr. Michal Kulich, PhD. Supervisor's e-mail adress: kulich(«)karlin.mff.cuni.cz Abstract: In the presented work we study elementary stochastic methods for modeling genetic populations. First we show some basic notion of general genetics for...
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Testing heteroscedasticity
Špaková, Mária ; Kalina, Jan (advisor) ; Zichová, Jitka (referee)
Title: Testing heteroscedasticity Author: Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jan Kalina Ph.D., Institute of Computer Science, Academy of Sciences of the Czech Republic Abstract: This paper deals with testing heteroscedasticity. It is divided into four chapters. The first three chapters focus on the theory and the last one is devoted to practical testing using specific data. In the beginning of the theoretical part, basic concepts, knowledge and relationships concerning the linear regression, the regression model and the estimation of parameters by the method of ordinary least squares are introduced. The rest of this part is devoted to heteroskedasticity, its consequences and solutions. The following heteroscedasticity tests are being discussed: Breusch - Pagan, Goldfeld - Quandt and White. The practical part contains actual applications of the described tests and other methods to detect heteroskedasticity using three examples: Outlays vs. income, GDP and Expenditures on food. The aim of this paper is to discuss the above-mentioned tests. Three examples on real data with economic motivation confirm the theoretical properties of the tests. A uniformly optimal test of heteroscedasticity does not exist and different tests yield rather different...
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Financial functions in Mathematica
Stacho, Michal ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The Mathematica software contains a fully integrated environment for a large number of instruments used in classical and modern finance. One of it`s basic capabilities is an advanced evaluation of the time value of money, then pricing of financial instruments such as bonds or financial derivatives and finally financial mapping with advanced library of technical indicators. Mathematica also provides immediate access to a large field of financial and economic data through external servers and offers financial tools for working with external data. This thesis deals with descriptions of the functions implemented in Mathematica, explaining the principle of their operation and application to real data.
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