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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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Combinatorial portfolio optimization
Zákutná, Tatiana ; Kopa, Miloš (advisor) ; Petrásek, Jakub (referee)
In this thesis, a portfolio optimization with integer variables which influence optimal assets allocation, is studied. At the beginning basic terms, measures of risk - variance, Value at Risk (VaR), Conditional Value at Risk (CVaR) are defined and the mean-risk models are derived for a practical application. Heuristics and standard algorithms of software GAMS are used for solving problems of the combinatorial portfolio optimization. Two types of the he- uristics are described: the Threshold Acceptance and the Genetic Algorithm. The heuristics are implemented in the MATLAB, applied on financial data and compared with an output of the software GAMS. 1
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Kelly criterion in portfolio selection problems
Dorová, Bianka ; Kopa, Miloš (advisor) ; Omelka, Marek (referee)
In the present work we study portfolio optimization problems. Introduction is followed by chapter 2, where we introduce the concept of utility function and its relationship to the investor's risk attitude. To solve the optimization problem we consider the Markowitz portfolio optimization model and the Kelly criterion, which are recalled in the fourth and fifth chapter. The work also contains an extensive numerical study. Using the optimization software GAMS we solve portfolio optimization problems. We consider a portfolio problem with (and without) allowed short sales. We compare the obtained portfolios and we discuss whether Kelly optimal portfolio is a special case of the Markowitz optimal portfolio for the special value of the minimum expected return.
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Multidimensional risk measures
Chromíková, Dana ; Kopa, Miloš (advisor) ; Cipra, Tomáš (referee)
This thesis deals with multiperiod risk measures and multiperiod models with these risk measures in the objective are formulated. Multiperiod models consider the possibility of an intermediate actions within the investment horizont and represent the real situation in a better way than one-period models. First the basic properties for one-period risk measures are summarized. Then multiperiod risk measures are de ned and several ways of construction concrete risk measures are discussed as extension of one-period risk measures. Multiperiod portfolio selection mean-risk models with di erent risk measures are formulated, transaction costs are included and short sales are not allowed. Using scenario approach the analysis on real data is performed and optimal strategies for one-period and multiperiod models are compared. A transaction costs e ect on optimal strategy is examined.
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Stochastic dominance portfolio efficiency measures
Jakubcová, Monika ; Dupačová, Jitka (referee) ; Kopa, Miloš (advisor)
In the present work we study the stochastic dominance portfolio e ciency measures. The investor's risk attitude is given by the type of an utility function. If this information is unknown or a general investor is assumed, it is possible to use the stochastic dominance principle, in which the portfolio is only classi ed as e cient or ine cient. We build on the works of Post, Kuosmanen and Kopa, who formulated the criteria of portfolio e ciency for nonsatiate and risk averse investors. On the basis of these criteria, we de ne the second-order stochastic dominance (SSD) portfolio e ciency measures. We examine the properties of SSD ine ciency measures, which allow to compare SSD ine cient portfolios. We prove mutual relationships for the de ned SSD ine ciency measures. Eventually, we test the SSD e ciency of a US market portfolio on real-world US Stock Exchange data.
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Measures for efficiency and eco-efficiency
Dzianová, Ivana ; Kopa, Miloš (referee) ; Lachout, Petr (advisor)
Comparison between the economic subjects on micro and macro economic levels by a unitary indicator is provided by measuring efficiency as an evaluation of the performance of subjects. For each economic subject technical, allocative, economic, scale efficiencies and eco-efficiency can be computed if all data required are available. This paper attends to examine a method based on linear programming - Data Envelopment Analysis (DEA). Two models for technical efficiency and their derivates to measure other efficiencies are presented and compared in detail - a simple DEA model and an additive DEA model. Finally, theoretical procedures are applied on the forest industry in between the counties of Czech Republic and comparison by measurements of efficiencies is provided.
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Applications of game theory in economy
Chvoj, Martin ; Prokešová, Michaela (referee) ; Kopa, Miloš (advisor)
Nt'izev prace: Aplikacc teorie her v ekonomii Aitlor: Martin Chvoj Katedra: Katedra pravdepodobnosli a matematicke statistiky Vedouci bakah'tfske prace: RNDr. Ing. Milos Kopa, PhD. e-mail vedoucilio: kopa@karlin.mfT.cuni.cz Ahstrttkt: Tato prace pojednava o leorii her a jeji aplikaci v ckonomicke teorii. Na zacatku pracc je deflnovan pojem ..lira N hraeu4', ktcry jc v dalsieh kapitolaeh rozvijen. Ncjprve jsou popsany zaklady klasicke nekooperalivni tcoric her opfraji'cf se o pojcm Nashovy rovnovahy a koopcrativnich her s durazein na jadro hry a Shaplcyho hodnotu. Dale jsou analy/ovany statisiickc hry, ktere se zabyvajf rozhodovanim hracu pfi riziku. 7 modcrnich pfistupii je zde popsana staticka a dynaniicka analyza evolucnich her. Dalsi cast je venovana ekonomickc aplikaci vscch defmovanych druhu her na teorii finny. V zaveru prace je popsan a vyhodnocen model, sinuilujiei cvolucnf vyvoj populace, uvnitf kterc je hrana lira zvana veznovo dilema s dobrovolnou ucasti. Klicovd slovci; teorie her, evolucni hry, bayesovske hry, oligopol Title: Applications of game theory in economics Author: Martin Chvoj Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ing. Milos Kopa, PhD. Supervisor's e-mail address: kopa^karlin.mfT.cuni.cz Abstract: This work deals with game theory...
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