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Selected applications of mathematics
KRATOCHVÍL, Daniel
The thesis is a contribution to the topic of game theory which belongs to the field of applied mathematics. The work is divided into three parts. In the first part, the basic terminology of game theory is introduced and subsequently applied in conflict mathematical model situations. The second part deals with the history of game theory and presents some historical problems as well as milestones in this area of mathematics. The last part is focused on different variants of NIM games, their analysis and the search for an optimal strategy.
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NIM and Mathametics
NĚMCOVÁ, Věra
The diploma thesis deals with the combinatorial game NIM. The work is divided into two parts - theoretical and practical. The theoretical part submits the Sprague-Grundy theorem (which is a general introduction to game theory) and the analysis of several substraction games. Then follows the NIM: the rules of the game, various analysis options, features, history, variants and mainly finding the winning strategy. It´s necessary to know binary system and NIM-sum. The practical part contains an analysis of several games played with students and wants to find out if they are able to intuitively discover some parts of the winning strategy.
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Mechanism of Negative Interest Rate's Influence on Bank Net Interest Margin
Fan, Yingxuan ; Holub, Tomáš (advisor) ; Jakubík, Petr (referee)
Net interest margin (NIM) is an important indicator of a bank's operational efficiency. Based on the balance sheet data of 189 major listed banks in Europe from 2010 to 2019, this thesis studies the bank's NIM mechanism in a negative interest rate environment. This thesis focuses on the system GMM method and the results show that the policy interest rate is positively related to NIM in the long run and negatively related in the short run, but the relationship between the two is not significant in the short run. Moreover, in a negative interest rate environment, bank NIM's sensitivity to policy interest rates has greatly increased, especially the policy of interest rate cuts. In addition, the sensitivity of NIMs of different banks to policy interest rates also differs significantly. Generally, the NIMs of banks with a high degree of internationalization and larger size are less sensitive to changes in policy interest rates, while the NIMs of banks with a higher share of retail business in their total business are more sensitive to changes in policy interest rates. Finally, through the value-at-risk analysis and stress test, this thesis concludes that the policy interest rate, net loan-to-asset ratio, non-performing loan ratio and inflation rate are sensitive factors of NIM. When NIM is subject to a...
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Game Theory for Gifted Secondary School Students
Skálová, Alena ; Hykšová, Magdalena (advisor) ; Staněk, Jakub (referee)
The thesis contains a textbook for gifted secondary school students. Its aim is to give to these students (or to their teachers) a Czech-written text covering fundamental principles in the field of game theory. In the first part we introduce the combinatorial games and some elementary methods of their solution. The second part is devoted to the game of Nim, to the Sprague-Grundy function and to the sums of the combinatorial games. It also contains a necessary introduction to the binary numeral system. In the third part we present the concept of matrix and bimatrix games. There is a lot of exercises and examples in the textbook. At the end we bring solutions to the most of them, providing the active reader with the opportunity of checking their own solutions.
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