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Robust filtering
Mach, Tibor ; Dostál, Petr (advisor) ; Štěpán, Josef (referee)
This work is focused on the problem of filtering of random processes and on the construction of a stochastic integral with a measureable parameter. This integral is used to devise filtration equations for a random process which is based on a model motivated by a financial application. The method used to devise them and the equations themselves are then compared with the so called optional filtering from the book Markov processes and Martingales by Rogers and Williams, while the definition of the optional projection is extended so it is possible to correct a~mistake in a proposition in the aforementioned book. Powered by TCPDF (www.tcpdf.org)
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Bayesian modeling of market price using autoregression model
Šindelář, Jan
1 Bayesian modeling of market price using autoregression model 1Šindelář Jan Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Miroslav Kárný, DrSc. Abstract: In the thesis we present a novel solution of Bayesian filtering in autoregression model with Laplace distributed innovations. Estimation of regression models with lep- tokurtically distributed innovations has been studied before in a Bayesian framework [2], [1]. Compared to previously conducted studies, the method described in this article leads to an exact solution for density specifying the posterior distribution of parameters. Such a solution was previously known only for a very limited class of innovation distributions. In the text an algorithm leading to an effective solution of the problem is also proposed. The algorithm is slower than the one for the classical setup, but due to increasing com- putational power and stronger support of parallel computing, it can be executed in a reasonable time for models, where the number of parameters isn't very high. Keywords: Bayesian, Autoregression, Optimal Trading, Time Series References [1] P. Congdon. Bayesian statistical modelling. Wiley, 2006. [2] A. Zellner. Bayesian and Non-Bayesian analysis of the regression model with multivari- ate Student-t error term. Journal...
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Bayesian Approaches to Stochastic Reserving
Novotová, Simona ; Pešta, Michal (advisor) ; Branda, Martin (referee)
In the master thesis the issue of bayesian approach to stochastic reserving is solved. Reserving problem is very discussed in insurance industry. The text introduces the basic actuarial notation and terminology and explains the bayesian inference in statistics and estimation. The main part of the thesis is framed by the description of the particular bayesian models. It is focused on the derivation of estimators for the reserves and ultimate claims. The aim of the thesis is to show the practical uses of the models and the relations between them. For this purpose the methods are applied on a real data set. Obtained results are summarized in tables and the comparison of the methods is provided. Finally the impact of a prior distribution on the resulting reserves is showed. Powered by TCPDF (www.tcpdf.org)
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Bayesian modeling of market price using autoregression model
Šindelář, Jan
1 Bayesian modeling of market price using autoregression model 1Šindelář Jan Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Miroslav Kárný, DrSc. Abstract: In the thesis we present a novel solution of Bayesian filtering in autoregression model with Laplace distributed innovations. Estimation of regression models with lep- tokurtically distributed innovations has been studied before in a Bayesian framework [2], [1]. Compared to previously conducted studies, the method described in this article leads to an exact solution for density specifying the posterior distribution of parameters. Such a solution was previously known only for a very limited class of innovation distributions. In the text an algorithm leading to an effective solution of the problem is also proposed. The algorithm is slower than the one for the classical setup, but due to increasing com- putational power and stronger support of parallel computing, it can be executed in a reasonable time for models, where the number of parameters isn't very high. Keywords: Bayesian, Autoregression, Optimal Trading, Time Series References [1] P. Congdon. Bayesian statistical modelling. Wiley, 2006. [2] A. Zellner. Bayesian and Non-Bayesian analysis of the regression model with multivari- ate Student-t error term. Journal...
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Robust filtering
Mach, Tibor ; Dostál, Petr (advisor) ; Štěpán, Josef (referee)
This work is focused on the problem of filtering of random processes and on the construction of a stochastic integral with a measureable parameter. This integral is used to devise filtration equations for a random process which is based on a model motivated by a financial application. The method used to devise them and the equations themselves are then compared with the so called optional filtering from the book Markov processes and Martingales by Rogers and Williams, while the definition of the optional projection is extended so it is possible to correct a~mistake in a proposition in the aforementioned book. Powered by TCPDF (www.tcpdf.org)
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What We Know About Monetary Policy Transmission in the Czech Republic: Collection of Empirical Results
Babecká Kucharčuková, Oxana ; Franta, Michal ; Hájková, Dana ; Král, Petr ; Kubicová, Ivana ; Podpiera, Anca ; Saxa, Branislav
This paper concentrates on describing the available empirical findings on monetary policy transmission in the Czech Republic. Besides the overall impact of monetary policy on inflation and output, it is useful to study its individual channels, in particular the interest rate channel, the exchange rate channel, and the wealth channel. The results confirm that the transmission of monetary impulses to the real economy works in an intuitive direction and to an intuitive extent. Our analyses show, however, that the global financial and economic crisis might have somewhat slowed and weakened the transmission. We found an indication of such a change in the functioning of the interest rate channel, where elevated risk premiums played a major role.
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Srovnání bayesovského a četnostního přístupu
Ageyeva, Anna ; Hebák, Petr (advisor) ; Vilikus, Ondřej (referee)
The thesis deals with Bayesian approach to statistics and its comparison to frequentist approach. The main aim of the thesis is to compare frequentist and Bayesian approaches to statistics by analyzing statistical inferences, examining the question of subjectivity and objectivity in statistics. Another goal of the thesis is to draw attention to the importance and necessity to teach Bayesian statistics at our University more profound. The thesis includes three chapters. The first chapter presents a Bayesian approach to statistics and its main notions and principles. Statistical inferences are treated in the second chapter. The third chapter deals with comparing Bayesian and frequentist approaches. The final chapter concerns the place of Bayesian approach nowadays in science. Appendix concludes the list of Bayesian textbooks and Bayesian free software.
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Konstrukce vícekrokových predikcí v normálním BVAR(p) modelu za použití Monte Carlo vzorkování
Šindelář, Jan
In Bayesian normal vector AR model (BVAR) of data evolution in a discrete time we are trying to predict the distribution of data up to horizon h. Since the analytical solution of such a prediction is difficult due to the high dimensionality of the problem, we are forced to search for approximative solutions. We propose a solution using Monte Carlo sampling from parameter distribution and later reconstruction of the predictive distribution of data.
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Zpřesnění modelu odhadování vývoje cen na komoditních trzích za pomocipřidání nových kanálů
Kozmík, V. ; Šindelář, Jan
Present work deals with a problem of price prediction on futures markets. Main goal of this work is to find out on which input channels (price,volume of contracts, etc.) depends the sought future price. We make further simplications to be able to present the problem as a mathematical one, which can be solved using Bayesian estimation methods. In this work we present the process of price prediction and then concentrate on the main aim, which is structure determination. Applied algorithm is described mathematically and also programmed in Matlab environment. The results of the algorithm on specific data and their economic interpretation are the last part of this work.
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