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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Continuous processes with quadratic varaition
 Svoboda, Miroslav ; Dostál, Petr (advisor) ; Dvořák, Jiří (referee)
The work is devoted to the properties of the continuous random processes with a compact index set that are having finite quadratic variation. In the thesis we define the stochastic Riemannn integral and then follow a development of a theory leading to deriving of Ito formula. The terms, concretely quadratic variation and Ito's formula and in the process are introduced using the konvergence in probability for the continuous random processes. The applied part of the thesis, starting in chapter 6, is considering an investor trading on the stock market. Using the Ito formula we will show that both the Black-Sholes and the bachelier models are modelling the fair price of the European call vanilla option, when the price of the share on the market is modelled by. Powered by TCPDF (www.tcpdf.org)
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Path analysis of Wiener Process
 Belyaeva, Evgeniya ; Hlubinka, Daniel (advisor) ; Seidler, Jan (referee)
In this thesis we research and introduce several properties of paths of a Wiener process. At first we present a way to prove existence of a Wiener process and then we discuss its basic properties. The second chapter is devoted to analytical properties of Wiener's paths including monotonicity, differentiability, Hölder continuity and quadratic variation. In the third chapter we research the reflection principle and the distribution of maxima of paths in the case of a random walk and then also in the case of a Wiener process. The fourth chapter concentrates on the Skorohod embedding and its application in the proof of the classic central limit theorem. Finally, using the results of the first chapter we simulate a path of a Wiener process and illustrate some of the properties discussed earlier. To demonstrate the concepts, several problems were included in the relevant chapters together with an author's solution. Powered by TCPDF (www.tcpdf.org)
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