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Economic applications of geometric programming
Štěpánek, Ladislav ; Dupačová, Jitka (advisor) ; Zimmermann, Karel (referee)
Geometric programming is a special case of nonlinear programming, where objective function and constraints are shaped as posynomials. In this work we introduce geometric programming and solving methods. In~last chapter we will apply the geometric programming to Cobb-Douglas production function, create a model with random demand and possible extensions of this model. Powered by TCPDF (www.tcpdf.org)
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Stochastic activity networks
Sůva, Pavel ; Dupačová, Jitka (advisor) ; Kaňková, Vlasta (referee)
In the present work, stochastic network models representing a project as a set of activities are studied, as well as different approaches to these models. The critical path method, stochastic network models with probability constraints, finding a reference project duration, worst-case analysis in stochastic networks and optimization of the parameters of the probability distributions of the activity durations are studied. Use of stochastic network models in telecommunications networks is also briefly presented. In a numerical study, some of these models are implemented and the~related numerical results are analyzed.
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Multiobjective portfolio optimization
Malá, Alena ; Kopa, Miloš (advisor) ; Dupačová, Jitka (referee)
The goal of this thesis is to summarize three basic principles of solving multi-objective programming problems. We focus on three approaches: a linear combination of objective functions, ε-constrained approach and a goal programming. All these methods are subsequently applied to US data. We consider monthly excess returns of ten US representative portfolios based on individual stock market capitalization of equity that serve as basic assets. Our aim is to find the efficient portfolios. Next we investigate a structure of these portfolios and their mutual relationships. Graphic representation of efficient frontiers is also included in the thesis. All calculations were performed using Mathematica software version 8.
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Probabilistic programs with discrete probability distributions
Murgaš, Karel ; Dupačová, Jitka (advisor) ; Branda, Martin (referee)
This thesis deals with stochastic programming problems with probabilistic constraits with discrete distribution. Finitness and corectness of algortithm for finding p-level efficient points is proved and I implement this algorithm in R. I relax the feasible set to get convex problem and I study properties of the relaxed set. Results for linear, integer and nonlinear problems are presented. In en example I compare discrete approach with the continuous one.
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Semidefinite programming and its applications
Chrenko, Jakub ; Dupačová, Jitka (advisor) ; Červinka, Michal (referee)
In the present work we study linear positive-semidefinite programming (SDP). We ilustrate applicability of this problem with a few examples and we introduce some other optimization problems as a part of this cathegory. SDP can be seen as a generalization of linear programming which indicates a possibility of building similar duality theory and other conclusions known in the case of linear programming. We introduce a family of path following first order algorithms as an example. Moreover we briefly describe a numerical solution of a practical example by recently developed software tools, which provide an accessible and effective solution for SDP.
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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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Value-at-Risk estimation - non standard approaches.
Picková, Radka ; Šmíd, Martin (referee) ; Dupačová, Jitka (advisor)
The topic of the presented work is Value-at-Risk (VaR) and its estimation. VaR is a financial risk measure and is defined as a quantile of the distribution of future returns, resp. losses. There exist various methods based on different assumptions how to estimate VaR. The most commonly used methods usually assume that the returns, resp. losses, are independently and identically distributed, especially that they are normally distributed. Since this assumption is not satisfied for most daily financial data, many alternative approaches have been suggested to estimate VaR. In the presented work two of them are discussed in detail, the CAViaR method and its asymptotic properties and the method of filtered historical simulation. One part of the work are numerical experiments with real data.
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