|
Using linear programming to solve Markov decision processes
Dotlačilová, Petra ; Kořenář, Václav (advisor) ; Fábry, Jan (referee)
The aim of this bachelor thesis is to develop and describe how to solve Markov decision processes with alternatives by using the methods of linear programming. The theoretical part describes Markov decision processes. The practical part builds and describes the mathematical model of linear programming processes for Markov decision processes with alternatives. The method used for the calculation of the processes is described with the help of a simplex method. The last section of the practical part studies how the optimal solution of the linear programming is influenced by the postoptimalization changes which modify the probability and revenue properties of the processes.
|
|
Essays on Mathematical Methods for Economics
Brázdik, František ; Kejak, Michal (advisor) ; Wieland, Volker (referee) ; Halická, Margaréta (referee)
In the first chapter, by introduction of output augmentation and input reduction I extend additive models for stochastic data envelopment analysis (SDEA), which were developed by Li (1998) to handle the noise in the data. Applying the linearization procedure by Li (1998) the linearized versions of models are derived. In the empirical part of this chapter, the efficiency scores of West Java rice farms are computed. The computed scores are compared to the stochastic frontier approach scores by Druska and Horrace (2004) and weak ranking consistency with results of stochastic frontier method is observed. The objectives of the second chapter are to evaluate technical and scale efficiency of rice farms in West Java and to identify determinants affecting farms' efficiency. Data Envelopment Analysis is used for estimation of technical efficiency scores. Additionally, Tobit regression is used to explain the variation in the efficiency scores by farm-specific factors. I conclude that the farm size is one of the most important factors of farm technical efficiency and that high land fragmentation was the main source of farm inefficiency during the final period of intensification era, known as Green Revolution. In the last, chapter I examine macroeconomic stability and the properties of business cycles in the model with...
|
|
Word Problems with Anti-signal for the Pupils of Primary School
Chaloupková, Sylva ; Hejný, Milan (advisor) ; Slezáková, Jana (referee)
Primary school, specifically on word problems with anti-signal. In the word problems there is often a word which points out an operation which has to be used for the solution the problem. For example words like add, upwards, ascend, get in, expand, ..., that refer to addition. Or words like reduce, thereunder, descend, get off, decrease, ..., that refer to subtraction. Those words are called signals. But if a word refers to opposite operation than the word is pointing out, we are calling the word as an anti-signal. This thesis inscribes research of the mathematical problems with antisignal among the pupils of Primary school. The greatest part of the work comes out from experiments, which are filed at videos, partly listed in protocols and analysed. The short part, questionnaires, tries to catch opinions of experienced teachers on méthodologie view of the problems with anti-signal. Finally the attention is paid to the presence of those problems in the sets of textbooks, which are usually used at Primary schools. Keywords: word problems, anti-signal, operator, address, pupil's thinking processes during solving
|
|
Optimization methods in finance
Baník, Peter ; Zichová, Jitka (referee) ; Hurt, Jan (advisor)
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.
|
|
Stochastic modellinf of epidemics
Vencálek, Ondřej ; Brabec, Marek (referee) ; Antoch, Jaromír (advisor)
Nazev prace: Stochasticke modelovani epidemii Autor: Oridfej Venealek Katedra: Katedra pravdepodobnosti a matenmticke sta.t.i.stiky Vedouci diplomove prace: Prof. RNDr. .Jaromi'r Antoch. CSe. e-mail vedoucfho: Jaromir.Antoch'3mff.cuni.c-/ Abstrakt: Tato diplomova prace se zabyva modelovanmi prevalence chfipky v Ceske repnb- lice v letech 2001 az 2003. Vychazi z dat laskave ZHpujccnych Statnhn zdravotm'm ustavem. Z hlediska epiclemiologie jde o observaeni deskriptivuf studii: zabyva se rozdelenhn poctu riernocnych chfipko\ v prnbehu sledovaneho ubdobi v ceske populaci. Matematiekym podkla- dem pro modelovaih je nelinearni hierarehicky model. Funkem tvar zavislo.sti prevalence na case vyehazt z teorie rustovyeh kfivek. Klicova slova: prevalence, sledovane obdobi, riistove kfivky, hierarehicky model Title: Stochastic- Modelling of Rpidemy Autor: (Jndrej Vencalek Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Jaronn'r Antoch, CSc. Supervisor's e-mail address: Jaromir.Antochl'0.|inff.ei.mi.cz Abstract: This diploma tbesis deals with modelling of prevalence of influenza in the C/ech Republic in the period from 2001 till 2003. It is based on data which were khidly lent by Statin' zdravotni nstav. This work is observational descriptive study from the view of epidemiology:...
|
|
Stochastic models for genetic analysis
Selementová, Martina ; Zichová, Jitka (referee) ; Kulich, Michal (advisor)
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...
|
|
Statistical investigation of CT pulmonary angiography in terms of development and depending on age and sex in District Kroměříž 2006-2010
OPLUŠTIL, Vladimír
CT pulmonary angiography is, together with ventilation-perfusion scintigraphy, the main diagnostic methods for recognition as pulmonary embolism. This is a very dangerous disease, which may end up even in death. Its share of deaths in hospitals, including subsequent ? complications, is around 4%. Therefore, emphasis is placed on early diagnosis. Clinical and laboratory symptoms are unspecific (including D Dimer).(10) Pulmonary embolism after ischaemic heart disease and arterial hypertension the frequency of its occurrence, the third most serious cardiovascular diseases. Cause of death in pulmonary embolism is usually the exhaustion of the right heart, seeking to overcome suddenly increased the resistance of the pulmonary circulation. This is the pulmonary artery or its branches is embolism blood clot-trombus, resulting in the venous system or in the heart, a saddle embolus, patched up a significant part of the lung. The most common place of trombs, which embolizated to the lungs, are deep veins of lower limbs if they are affected by the flebotrombolitis.(16) In addition to the acute embolism are frequent and chronic embolism. They are equally dangerous. By gradually and subtly clog small blood vessels, reduces the total cross-sectional area of open pulmonary artery, which have blood flow, and since the volume of blood must be maintained even in the smaller section of the vascular bed, should permanently increase the blood pressure in a small circulation, which is also dangerous.(16) In my work is the methods of mathematical statistics processed file 1966 CT pulmonary angiogramy (CTPA), carried out on the CT work in Kroměříž in the years 2006-2010. The work is focused on the statistical survey of the influence of age, sex, and the time evolution of the CTPA during that period.
|
|
Stabilita úloh stochastického programování s lineární kompenzací
Kaňková, Vlasta
Stochastic programming problems with recourse is a composition of inner and outer optimization problems. A solution of the outer problem depends on the "underlying" probability measure, a solution of inner problem depends on the solution of the outer problem and on the random element realization. Consequently (in the case of the optimal solution of the outer problem) the optimal value and the solution of the inner problem depend also on the probability measure. The aim is to investigate this dependence.
|
|
Hydraulic calculation of sewage system in Lipůvka
Balas, Jan ; Raček, Jakub (referee) ; Hluštík, Petr (advisor)
Diploma thesis is focused on hydraulic assessment of Lipůvka´s sewer system, done by dynamic rainfall-runoff simulation model. Because of this fact, chapter about mathematical models is included. Commonly used programs to this actions are listed as well. Next part of the thesis describes monitoring campaign, which was done in Lipůvka and results are used to calibrate the simulation model. Hydraulic assessment of sewer system by this calibrated model was done.
|
|
Implied Volatility and Smile
Rojček, Jakub ; Pígl, Jan (advisor)
In this work author speaks a little in generic about financial derivatives. Then he derives the famous Black-Scholes formula using less precise mathematical apparatus. Afterwards, he will analyze a few volatility models and their applications for creating volatility surface, which is the main goal of both theoreticians and practitioners. As we will see, the theory is yet very deep but unconsolidated. Nevertheless, praxis has gained some nearly sufficient approaches.
|
guest ::
