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Price of Volatility of Financials Assets
Gříšek, Lukáš ; Černý, Michal (advisor) ; Chrobok, Viktor (referee)
This diploma thesis describes problem of change-points in volatility of the time-series and their impact on price of nancial assets. Those change-points are estimated by using statistical methods and tests. Change-point estimation was tested on simulated datas and real world driven datas. Simulation helped to discover signi cant characteristics of change-point test, those data were simulated with using stochastic calculus. Google share prices and prices of call options were chosen to analyse impact of volatility change on those prices. Also implied volatility and its impact to call option price was analysed.
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Constraint Programming as Means for Solving Discrete Problems
Janečková, Jitka ; Fábry, Jan (advisor) ; Černý, Michal (referee)
Application of constraint programming (CP) is one of the possible ways of solving discrete problems. It can be used for both search for feasible solution and optimization. CP offers a whole range of approaches for either a solution search or for acceleration of the process of its search -- from search algorithms or consistency techniques to propagation algorithms, which are basically only a combination of the two preceding methods. For optimization we most often use branch and bound approach, which differs in some aspects from a method of the same name used in mathematical programming (MP). Comparison of CP and MP is interesting in many other aspects. With CP the formulation of problems is more flexible, which allows for creation of often simpler and smaller models. On the other hand, its disadvantage is a limited use: Constraint satisfaction (optimisation) problem, as we call the constraint programming problem, cannot contain any discrete variables. CP is suitable especially for problems with a lot of constraints and only few variables, ideally only two. In the beginning, the paper introduces the basic terms of constraint programming, then it describes algorithms and techniques used for solving discrete problems and compares CP with mathematical programming.
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The Bankruptcy Rules in Linear Ordered Structures
Muchna, Jan ; Pánková, Václava (advisor) ; Černý, Michal (referee)
The bankruptcy problem involves the distribution of perfectly divisible goods. Particular attention is paid to the situations, where the amount of goods available is not enough to cover the demand. An example of real life situations that can be solved using various bankruptcy rules may be a division of a heritage or when a company goes bankrupt and its estates are sold to satisfy interested parties' claims. This paper introduces to the problem a linear structure of the participants, meaning that participants are now satisfied one after another in a preset order. It applies the equal awards (CEA) and the equal losses (CEL) solutions on the revised problem. Since their axiomatization is no longer valid, both solutions are extended and new characterizations are given in the thesis. The thesis contains a series of original proofs for both extended solutions and whole problem is examined in the setting of the well-known river sharing problem.
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Solving vehicle routing problems and algorithm implementation on GPU
Hájek, Jan ; Fábry, Jan (advisor) ; Černý, Michal (referee)
A very wide-ranging subgroup of vehicle routing problems from the graph theory is a common and frequent problem handled daily by transport companies, airline businesses, hi-tech companies with planning drilling of printed circuits boards or other companies from different industries. During numerous previous researches of these problems a lot of analyses were made and many solutions proposed -- of which an outline is in this paper. Some of them giving better or worse results in longer or shorter computing time. In spite of the fact that the processors and new technologies performance is increasing, with some algorithms we cannon compute the result in a reasonable time. That is why this paper is asking a question, if there can be found a fitting algorithm which could be applied on different and faster processing unit structures so it could be ensured a multiple computing speed increase so far. The analysis was carried out using computer experiments on a new build and implemented branch and bound algorithm with a matrix rate reduction.
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Evaluation of properties of pyrolysed resins
Halasová, M. ; Chlup, Zdeněk ; Strachota, Adam ; Černý, Martin ; Dlouhý, Ivo
The presented work describes mechanical properties of materials prepared by pyrolysis of polysiloxane resins. The polymeric precursors had different chemical composition. Materials under investigation are predetermined as a matrix for high temperature resistant long fibre composites. An instrumented hardness tester was employed for materials characterisation. The Vickers hardness, Martens hardness and indentation elastic modulus were the key parameters determined from the load-indentation depth curves. Influence of the mechanical properties on the ratio of T and D was established. Indents were observed by using confocal laser microscope.
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