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High-order stochastic dominance
Mikulka, Jakub ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
The thesis deals with high-order stochastic dominance of random variables and portfolios. The summary of findings about high-order stochastic dominance and portfolio efficiency is presented. As a main part of the thesis it is proven that under assumption of both normal and gamma distribution the infinite-order stochastic dominance is equivalent to the second-order stochastic dominance. The necessary and sufficient condition for the infinite-order stochastic dominance portfolio efficiency is derived under the assumption of normality. The condition is used in the empirical part of the thesis where parametrical approach to the portfolio efficiency is compared to the nonparametric scenario approach. The derived necessary and sufficient condition is based on the assumption of normality; therefore we use two sets of data, one with fulfilled assumption of normality and the other for which the assumption of normality was unambigously rejected. Consequently, the influence of fulfillment of the normality assumption on the results of the necessary and sufficient condition for portfolio efficiency is estimated.
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Exponential smoothing
Mikulka, Jakub ; Hanzák, Tomáš (advisor) ; Cipra, Tomáš (referee)
Nazev prace: Exponencialnivyrovnavani Autor: Jakub Mikulka Katedra: Katedra pravdepodobnosti a matematicke statistiky Vedouci bakalarske prace: Mgr. Tomas Hanzak e-mail vedouciho:hanzak@karlin.mff.cuni.cz Abstrakt: Prace se zabyva dvema metodami exponencialniho vyrovnavani pro nesezonni casove rady s lokalne linearnim trendem: Holtove metode a dvojitemu exponencialmmu vyrovnani (Brownove metode). Je ukazano, ze Brownova metoda je specialnim pnpadem Holtovy metody. Dale je uveden vztah procesu ARIMA(0, 2, 2) a Holtovy metody. Hlavni casti prace je teoreticke odvozeni hodnoty MSE a autokorelacniho koeficientu pfedpovedmch chyb Q pri pouziti Holtovy metody pro vsechny kombinace jejfch vyrovnavacich konstant za predpokladu generovani rady procesem ARIMA(0, 2, 2} pro vsechny hodnoty jeho parametru. Odvozene teoreticke vzorce jsou aplikovany tez na Brownovu metodu. Odvozene vzorce jsou pomoci simulaci overeny a vyzkouseny na realnych casovych radach. Jsou formulovany prakticke zavery tykajici se obou metod. Klicova slova: autokorelacni koeficient predpovednich chyb, Holtova metoda, dvojite exponencialni vyrovnavani,MSE, vyrovnavaci konstanty Abstract Title: Exponential smoothing Author: Jakub Mikulka Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomas Hanzak...
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High-order stochastic dominance
Mikulka, Jakub ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
The thesis deals with high-order stochastic dominance of random variables and portfolios. The summary of findings about high-order stochastic dominance and portfolio efficiency is presented. As a main part of the thesis it is proven that under assumption of both normal and gamma distribution the infinite-order stochastic dominance is equivalent to the second-order stochastic dominance. The necessary and sufficient condition for the infinite-order stochastic dominance portfolio efficiency is derived under the assumption of normality. The condition is used in the empirical part of the thesis where parametrical approach to the portfolio efficiency is compared to the nonparametric scenario approach. The derived necessary and sufficient condition is based on the assumption of normality; therefore we use two sets of data, one with fulfilled assumption of normality and the other for which the assumption of normality was unambigously rejected. Consequently, the influence of fulfillment of the normality assumption on the results of the necessary and sufficient condition for portfolio efficiency is estimated.
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Exponential smoothing
Mikulka, Jakub ; Cipra, Tomáš (referee) ; Hanzák, Tomáš (advisor)
Nazev prace: Exponencialnivyrovnavani Autor: Jakub Mikulka Katedra: Katedra pravdepodobnosti a matematicke statistiky Vedouci bakalarske prace: Mgr. Tomas Hanzak e-mail vedouciho:hanzak@karlin.mff.cuni.cz Abstrakt: Prace se zabyva dvema metodami exponencialniho vyrovnavani pro nesezonni casove rady s lokalne linearnim trendem: Holtove metode a dvojitemu exponencialmmu vyrovnani (Brownove metode). Je ukazano, ze Brownova metoda je specialnim pnpadem Holtovy metody. Dale je uveden vztah procesu ARIMA(0, 2, 2) a Holtovy metody. Hlavni casti prace je teoreticke odvozeni hodnoty MSE a autokorelacniho koeficientu pfedpovedmch chyb Q pri pouziti Holtovy metody pro vsechny kombinace jejfch vyrovnavacich konstant za predpokladu generovani rady procesem ARIMA(0, 2, 2} pro vsechny hodnoty jeho parametru. Odvozene teoreticke vzorce jsou aplikovany tez na Brownovu metodu. Odvozene vzorce jsou pomoci simulaci overeny a vyzkouseny na realnych casovych radach. Jsou formulovany prakticke zavery tykajici se obou metod. Klicova slova: autokorelacni koeficient predpovednich chyb, Holtova metoda, dvojite exponencialni vyrovnavani,MSE, vyrovnavaci konstanty Abstract Title: Exponential smoothing Author: Jakub Mikulka Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomas Hanzak...
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Occurrence of invasive species Eragrostis albensis in Prague and its surroundings
Mikulka, Jakub ; Holec, Josef (advisor) ; Jursík, Miroslav (referee)
Eragrostis albensis is an invasive weed. For invasive species it is typical that they are easily spread in to all manner of localities. Eragrostis albensis is recently described species, which spreads along the Elbe and the Vltava river. The purpose of this bachelor thesis was to find new places of occurrence in Prague and its surrounds and especially around the Vltava river. There were found a few locations where the occurrence of Eragrostis albensis was confirmed and these areas were always ruderal. At most of the areas there were maximum 3 plants. Only in one locality there were over 70 plants of Eragrostis albensis (locality Dvořákovo nábřeží). This invasive weed has wide ecological amplitude, it occurs especially on embankment nearby river, but it can also grow on pavements affected by dry. This species well tolerate disturbed areas and floods can help this weed to create new suitable locations. According to this monitoring it´s obvious, that Eragrostis albensis is a part of some ruderal districts in Prague.
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Sázení na loterie a sportovní události z pohledu behaviorální ekonomie
Mikulka, Jakub ; Koblovský, Petr (advisor) ; van Koten, Silvester (referee)
This thesis deals with the relationship between mood and behavior of bettors using a dataset provided by a betting company, Chance a.s., which operates in the Czech Republic. We consider three types of proxies for the mood: weather in regions, sport successes and the results of elections, and we build a fixed effect model to estimate the effect of mood on betting behavior. We provide strong evidence that the weather proxy has a significant effect on daily turnovers of the betting company and there also seems to be an effect of sport optimism. On the contrary, we failed to find any impact of elections. The results show that better mood tend to discourage clients from sports and lottery betting which is consistent with the increase in risk aversion or the depletion of a common self-control resource due to active mood regulation attempts. Additionally, we provide an evidence that the intra-month cycle in turnovers corresponds to liquidity constraint of bettors which disproves the permanent income hypothesis.
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Processes of real and nominal convergence in enlarged EU
Mikulka, Jakub ; Bič, Josef (advisor) ; Abrhám, Josef (referee)
This bachelor thesis deals with real and nominal convergence in the European Union. Particular attention is devoted to differences in convergence processes between New and Old Member States of the European Union. Beta and sigma convergence is tested at the levels of states, regions NUTS 1 and NUTS 2 during period 1995-2006. The results are put in theoretical background of Solow-Swan model and New Economic Geography. Furthermore, Balass-Samuelson effect and his incidence is presented.
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