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Scenario structures in multistage stochastic programs
Harcek, Milan ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multi-stage stochastic programming in the context of random process representation. Basic structure for random process is a scenario tree. The thesis introduces general and stage-independent scenario tree and their properties. Scenario trees can be also combined with Markov chains which describe the state of the system and determine which scenario tree should be used. Another structure which enables reduce the complexity of the problem is a scenario lattice. Scenario generation is performed using moment method. Scenario trees are used for representation of random returns as the input to the investment problem.
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Network flows in scheduling problems
Rubín, Daniel ; Branda, Martin (advisor) ; Lachout, Petr (referee)
The goal of scheduling problems is to assign machines to a pre-specified jobs which require processing. Standard approach leads to integer programming pro- blems where machine assignment is represented by binary variables. However, the resulting problems are of high time complexity. Formulating the scheduling problems in terms of network flows shows to be a more effective approach. The aim of this thesis is to introduce basic scheduling tasks and methods used to formulate them in terms of network flows. By means of total unimodularity, we show that network flow algorithms are suitable for solving such problems. Finally, the results are demonstrated in a numerical study. 1
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Benders decomposition in optimization
Minaříková, Michaela ; Branda, Martin (advisor) ; Rusý, Tomáš (referee)
The Bachelor thesis is dealing with Benders decomposition in optimization, especially in stochastic linear programming. In the begining the reader will be introduced to the important terms used in the decomposition algorithm. Con- sequently it is demonstrated how to reformulate the problem of stochastic linear programming to a special structure suitable for Benders decomposition. In the third chapter, the decomposition algorithm, using the feasibility and optimality cuts, is explained including conditions of convergence of the algorithm. There follows modification of algorithm for two stage stochastic linear programming. Finally, we illustrate Benders algorithm on two smaller problems. 1
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Portfolio optimization using risk premia
Novotná, Tereza ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
The main topic of this thesis is Portfolio Optimization Using Risk Premia. Basic terms are defined there such as utility function, investor's risk aversion, risk premia, absolute risk aversion measure and portfolio optimization. There are also stated important theorems about risk aversion. For better understanding, there can be found few examples. At the end of this thesis is shown empirical study. It presents how the restriction of risk premia affects optimal investment and other numerical results.
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Bilevel optimization problems and their applications to portfolio selection
Goduľová, Lenka ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
Title: Bilevel optimization problems and their applications to portfolio selection Author: Lenka Godul'ová Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D. Abstract: This work deals with the problem of bilevel tasks. First, it recalls the basic knowledge of mean-risk models, risk measure in singlelevel problems, and second degree stochastic dominance. Then it presents basic knowledge of bilevel tasks. bilevel problems have several advantages over singlelevel. In one process, it is possible to analyze two different or even conflicting situations. The bilevel role can better capture the relationship between the two objects. The main focus of the thesis is the formulation of various bilevel tasks and their reformulation into the simplest form. The numerical part deals with four types of formulated bilevel problems at selected risk measures. Keywords: Bilevel problems, Second degree stochastic dominance, Risk measures 1
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Risk quantification in annuity insurance
Berdák, Vladimír ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
The thesis examines the impact of individual risks on an annuity product. It focuses on the deffered whole life annuity and on two basic risks, which affect the overall loss the most. These are interest rate risk and longevity risk. We choose standard deviation (σ), value at risk (VaR) and expected shortfall (ES) at different confidence levels for target risk measures. Hoeffding decomposition is used to split the overall loss. Then Euler allocation principle will show the distribution of individual risks for different entry ages.
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Risk quantification in annuity insurance
Berdák, Vladimír ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
The thesis examines the impact of individual risks on an annuity product. It focuses on the deffered whole life annuity and on two basic risks, which affect the overall loss the most. These are interest rate risk and longevity risk. We choose standard deviation (σ), value at risk (VaR) and expected shortfall (ES) at different confidence levels for target risk measures. Euler allocation principle and Hoeffding decomposition are used to split the overall loss. These methods will show the distribution of individual risks for different entry ages.
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Reinsurance optimization using stochastic programming and risk measures
Došel, Jan ; Branda, Martin (advisor) ; Cipra, Tomáš (referee)
Title: Reinsurance optimization using stochastic programming and risk measures Author: Jan Došel Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Martin Branda, Ph.D., Department of Probability and Mathe- matical Statistics Abstract: The diploma thesis deals with an application of a stochastic progra- mming in a reinsurance optimization problem in terms of a present regulatory framework of the insurance companies within the European Union, i.e. Solvency II. In this context, the reinsurance does not only transfer a portion of the risk to the reinsurer but also reduces an amout of required capital. The thesis utilizes certain risk measures and their properties, premium principles and non-linear in- teger programming. In the theoretical part, there are basic terms from Solvency II, reinsurance, risk measures and the comonotonicity of random variables descri- bed and the optimization problem itself is derived. The approach is then applied in the practical part on data of Czech Insurers' Bureau using the GAMS software. Finally, a stability of the solution is tested depending on several parameters. Keywords: reinsurance optimization, stochastic programming, Solvency II, risk measures 1
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Image of Spain and Portugal in English written travelogues in 1750'
Branda, Martin ; Křížová, Markéta (advisor) ; Černá, Jana (referee) ; Erdösi, Péter (referee)
in English The master thesis is concerned with the analysis and interpretation of English written travelogues of the second half of the 18th century, which described Spain and Portugal. I work with two original texts and one translation from Italian, all the texts which were popular among their readers. The main goal of the thesis is to create the complex image of both respective countries and their inhabitants, based on the analysis of travelogues. During the analysis, I use the concept of stereotype as defined by Walther Lippmann. I also use so-called Black Legend, the negative view of the Iberian Peninsula originating in the 16th century. At the same time, the aim of the thesis is to compare the images in all works and come to more general conclusions about English perception of Spain and Portugal. Keywords: Spain, Portugal, travelogues, image of the Other, Black Legend, Southey, Baretti, Young
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Fixed interval scheduling problems - stochastic extensions, formulations and algortihms
Leder, Ondřej ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
Fixed interval scheduling problems have wide range of practical use in production planning, transportation, in hospitals or in schools when planning timetables. When solving these problems we often encounter requirement of integrality of solutions. Ignoring this condition is often not possible. In this thesis we propose some formulations of scheduling problems and their stochastic extensions. We also propone a new formulation of stochastic FIS problem, for which integrality of solution is byproduct of its definition. We present Gâteaux derivative and its relationship to stability of optimal value function of stochastic optimization problems under the influence of contamination. We propose a new theorem on the stability of such functions for fixed interval scheduling problems.
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