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Stochastic optimization models for energy trading
Klyuchevskiy, Iakov ; Lachout, Petr (advisor) ; Branda, Martin (referee)
Energy market modelling is one of the most pressing topics. There are several ways how to create the models depending on what features to expect and require. The thesis will be devoted to studying stochastic models of the energy market. We explain first the mechanics and the characteristics of the energy market. We then move on to two commonly used stochastic power price models with different options for volatility and the distribution of spikes. A comparison of the models then shows that some are significantly better than others. Further, two other models (and their modifications) were proposed based on the first four. One of them has shown good performance and can be advised for use in ELIX price modelling. 1
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Optimization problems solving using various software
Petráš, Tomáš ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with practical problems when solving tasks of linear programming using mathematical software Mathematica, Gams, R and Matlab. It describes the basic properties of solvers, packages and optimizing functions of these programs. The aim of the thesis is to compare computer times needed to solve problems of different sizes using the considered programs. We consider these time efficiencies with and without the time consumed by loading the input data. At the end of the thesis we find the most suitable program for each of the problems sizes and we give some recomendations for the practical use of these products when solving problems of linear programming.
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Conic optimization: theory and applications
Dortová, Zuzana ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
1 This work discusses the roles of second-order cone programming, these tasks are a special class semidefinitního programming. The work summarized basic de- finitions, properties and claims known about these tasks. Special attention is paid to methods of solving SOCP problems. In the last part of the paper are formu- lated in some special tasks of mathematical programming (linear programming, quadratic programming, ...) as special cases of SOCP problems.
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Statistical analysis of interval data
Troshkov, Kirill ; Antoch, Jaromír (advisor) ; Branda, Martin (referee)
Traditional statistical analysis starts with computing the basic statisti- cal characteristics such as the population mean E, population variance V , cova- riance and correlation. In computing these characteristics, it is usually assumed that the corresponding data values are known exactly. In real life there are many situations in which a more complete information can be achieved by describing a set of statistical units in terms of interval data. For example, daily tempera- tures registered as minimum and maximum values offer a more realistic view on the weather conditions variations with respect to the simple average values. In environmental analysis, we observe a pollution level x(t) in a lake at different mo- ments of time t, and we would like to estimate standard statistical characteristics such as mean, variance and correlation with other measurements. Another exam- ple can be given by financial series. The minimum and the maximum transaction prices recorded daily for a set of stocks represent a more relevant information for experts in order to evaluate the stocks tendency and volatility in the same day. We must therefore modify the existing statistical algorithms to process such interval data. In this work we will analyze algorithms and their modifications for computing various statistics under...
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Logistic regression with applications in financial sector
Bílková, Kristýna ; Branda, Martin (advisor) ; Pešta, Michal (referee)
In this bachelor thesis binary logistic regression model is described. Its parameters are estimated by maximum likelihood method. Newton-Raphson's algorithm is used for enumeration of these estimates. There are defined some statistics for testing the significance of the coefficients. Then stepwise regression is desribed. For assessing the quality of the model Pearson's Chi Square Test and Hosmer-Lemeshow's Test of the goodness of fit are defined. Diversification abilitz of the model is illustrated bz the Loreny curve and is quantificated by Gini coefficient, Kolmogorov-Smirnov statistics and generalized coefficient of determination. The theoretical knowledge is applied to insurance area data.
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Stable distribution and application to finance
Omelchenko, Vadym ; Klebanov, Lev (advisor) ; Branda, Martin (referee)
Title: Stable distributions and application to finance Author: Vadym Omelchenko Department: Department of Probability and Mathematical Statistics Supervisor: Prof. Lev Klebanov, DrSc. Supervisor's e-mail address: Lev.Klebanov@mff.cuni.cz Abstract: This work deals with the theory of the stable distributions, their parameter estimation, and their financial application. There arc given the methods of characteristic function and method of projections, which is rel- ative to ML-methodology, for estimation of the parameters of stable dis- tributions. We compare these methods with the conventional estimators. The quality of estimators is verified by the simulation of the sample having stable distribution with known parameters and comparing the estimates of these parameters with their real values. The aim of this work is estima- tion of parameters of the stable laws which iy applicable for modification of AHCH/GAHCH models with stable innovations. Keywords: stable distribution, ARGII/GARCII models, characteristic func- tion (CF) based estimators, maximum likelihood projection (MLP) estima- tors.
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Economic scenarios in insurance
Krýcha, Daniel ; Branda, Martin (advisor) ; Hurt, Jan (referee)
In this thesis we will focus on interest rate modelling and related practical aspects. We will explain the significance of generated scenarios of interest rate's movement for economic results of both life and non-life insurance companies. We will analyse presently known ways of approaching this matter and describe the selected models in detail. Taking into consideration the practical focus of this thesis, we will address the applied methods of model's calibration. Furthermore, we will employ these methods in an extensive numerical study, that will aim to reveal the weaknesses and strengths of particular calibration methods while implementing a specific model and to evaluate their potential application in actuarial practice. Central model of this work is CIR (Cox-Ingersoll-Ross) model.
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Solving mixed-integer linear programming problems in GAMS
Škoda, Štěpán ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
In the present work we study the problems of integer linear optimi- zation, at first from the theoretical point of view (Part I) and subsequently on the basis of empirical data (Part II). First section explains with what this field deals with and where is applied. Other sections contain annotated mathematical formulation of problems, definitions and theorems needed to understand the general methods for solving integer linear programs. In the last section of Part I, we introduce the two best known groups of algorithms that are used by commercial software. The second part provides more details on an Internet library that contains some practical problems, that has been needed to be solved in the past. Furthermore, there are sections dealing with solvers and the advanced options of GAMS. The last section presents data obtained in the course of solving problems using several codes (solvers) of software. 1
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