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Anelastic deformation of planetary bodies
Vach, Dominik ; Čadek, Ondřej (advisor) ; Běhounková, Marie (referee)
Observations indicate an existence of subsurface oceans for some of the icy moons in the Solar System which are heated by the tidal forces. In order to describe this anelastic deformation, the methods well-known from the continuum mechanics were employed, and thus the dissipation was calculated for various bodies. In the thesis, Maxwell and Kelvin-Voigt model were compared in their ability to predict the heating power of the bodies. In contrast to the Maxwell model, the Kelvin-Voigt model, which is generally not used in geophysics, repre- sents reversible processes, and thus could explain the effects which are otherwise explained only by the gravity. A program in Fortran was developed in order to compare the models by modelling 3D anelastic deformation of planetary bodies under the effect of tidal forces. The results indicate the predicted power can be various for both models and Kelvin-Voigt model could be used e.g. to describe short run deformation processes. 1
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Surface manifestation of melting within the ice shell of Europa
Vach, Dominik ; Kalousová, Klára (advisor) ; Velímský, Jakub (referee)
One of the most interesting extraterrestrial bodies in the Solar System is Europa, the icy satellite of Jupiter. This icy moon might have a sufficiently hospitable environment which could be harbouring life in the subsurface ocean deep under its icy crust. The thesis thoroughly examines the generation process of one of the surface formations called chaotic terrains. These huge areas of ice disruptions which uniquely characterize Europa's surface might play a significant role in the understanding of the inner structure of the moon. The latest research assumes the chaotic terrains form above liquid water lenses perched relatively shallow in the ice shell, however, no numerical simulations have been performed to confirm this theory. The goal of the thesis is to create a model which would validate the theory and explain the formation process of the chaotic terrains. The thesis runs several simulations, and our results suggest these water lenses and the process in the mantle might play a key role in the chaotic terrains formation.
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Artificial Neural Networks in Option Pricing
Vach, Dominik ; Gapko, Petr (advisor) ; Červinka, Michal (referee)
This thesis examines the application of neural networks in the context of option pricing. Throughout the thesis, different architecture choices and prediction parameters are tested and compared in order to achieve better performance and higher accuracy in option valuation. Two different volatility forecast mechanisms are used to compare neural networks performance with Black Scholes parametric model. Moreover, the performance of a neural network is compared also to more advanced modular neural networks. A new technique of adding rational prediction assumptions to neural network prediction is tested and the thesis shows the importance of adding virtual options fulfilling these assumptions in order to achieve better training of the neural network. This method comes out to increase the prediction power of the network significantly. The thesis also shows the neural network prediction outperforms the traditional parametric methods. The size and number of hidden layers in a neural network is tested with an emphasis to provide a benchmark and a structured way how to choose neural network parameters for future applications in option pricing. JEL Classification C13, C14, G13 Keywords Option pricing, Neural networks, Modular neu- ral networks, S&P500 index options Author's e-mail vach.dominik@gmail.com...
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Anelastic deformation of planetary bodies
Vach, Dominik ; Čadek, Ondřej (advisor) ; Běhounková, Marie (referee)
Observations indicate an existence of subsurface oceans for some of the icy moons in the Solar System which are heated by the tidal forces. In order to describe this anelastic deformation, the methods well-known from the continuum mechanics were employed, and thus the dissipation was calculated for various bodies. In the thesis, Maxwell and Kelvin-Voigt model were compared in their ability to predict the heating power of the bodies. In contrast to the Maxwell model, the Kelvin-Voigt model, which is generally not used in geophysics, repre- sents reversible processes, and thus could explain the effects which are otherwise explained only by the gravity. A program in Fortran was developed in order to compare the models by modelling 3D anelastic deformation of planetary bodies under the effect of tidal forces. The results indicate the predicted power can be various for both models and Kelvin-Voigt model could be used e.g. to describe short run deformation processes. 1
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Spatial agent-based models of common pool resources
Vach, Dominik ; Gregor, Martin (advisor) ; Červinka, Michal (referee)
This thesis examines the application of the spatial aspect applied in the com- petitive models in the context of the natural resource economics. At first, the spatial models are thoroughly derived in one dimension. Then also their general properties such as the choice of the agents' location or their payoff function are examined. These properties are investigated for various distri- butions of the resource, and therefore they depend also on their parameters. The Nash equilibrium and local stability conditions are derived for the basic setups. In the second part, these competitive models are numerically tested also in a two-dimensional space. One of the results also suggests, that in the setup where the players have perfect information, the beginning player is not necessarily always better off than the second player. Throughout the entire thesis it is also comprehensively examined whether the existence of corners of the strategy space has an impact on the existence of the competition which was successfully demonstrated on several cases. JEL Classification Q20, Q22, C62, C68, C72 Keywords spatial models, natural resource exploitation, Nash equilibrium, fishery, computer simulations Author's e-mail vach.dominik@gmail.com Supervisor's e-mail martin.gregor@fsv.cuni.cz 1
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