
Poisson process and renewal processes as claim frequency models
Ernst, Lukas ; Kříž, Pavel (advisor) ; Karafiátová, Iva (referee)
This bachelor's thesis focuses on modeling claim frequency, examining the Poisson process and its generalization, the renewal process. The first part of the thesis analyzes the Poisson process, while the second part delves into the renewal process and its asymp totic properties. The aim of the thesis is to provide a comprehensive view of the issue from a mathematical perspective and is complemented by a simulation study. 1


Mean Variance Optimization for Minimal Entropy Measure
Pustějovský, Zdeněk ; Večeř, Jan (advisor) ; Kříž, Pavel (referee)
It can be shown that linear transformations of logarithm are the only utility functions whose optimal portfolios do not depend on numeraire. This thesis focuses on maximiza tion of expected logarithmic utility of a general portfolio. We show that, given our market opinion represented by a state price density, the optimal expected payoff is the Kullback Leibler divergence of the market state price density and the numeraire state price density. In an incomplete market however, the market density may not be replicable and the best we can do is to find the portfolio with the smallest KL divergence to the market density. This problem does not have a general analytical solution and may not be numerically feasible for large portfolios but can be approximated, in two different ways, by a mean variance problem that do have such solutions. We demonstrate this approach on simple portfolios of 2 assets and one or two maximal contracts, that are just shifted European options and finally we point out some option strategies that can be used to partially hedge the portfolio against certain market scenarios. 1


Discretetime Girsanov theorem
Kremla, Tomáš ; Čoupek, Petr (advisor) ; Kříž, Pavel (referee)
This bachelor's thesis deals with the Girsanov theorem in discrete time, which has wide applications, for example in financial mathematics or filter theory. This theorem talks about the construction of a probability measure with respect to which a given process is a martingale up to a finite time. In this paper, Girsanov theorem is generalized to other types of processes and it is shown that these results correspond. Subsequently, a probability measure is constructed under which the entire process is a martingale. Finally, some sufficient conditions for absolute continuity of this new measure with respect to the original one are given. 1


The Study of Product Lifecycle Management in an Enterprise
Kříž, Pavel ; Gabrhelíková, Zdeňka (referee) ; Jurová, Marie (advisor)
The thesis explores sustainable development of a company focusing on PLM system in the environment of an industrial company. In the theoretical part the lifecycle of a product (PLM) is described as well as its demands and benefits focusing on the area of mechatronics. The following analysis of current IT environment gives information which is used as the basis for adjustments of the current system in a way to eliminate narrow places of the slim production of the company, avoid wasting and achieve sustainable development of the company while using current technologies.


Analysis of structural and proportional criteria of Romanesque and PreRomanesque rotundas.
Kříž, Pavel ; Kalousek, Lubor (referee) ; Unger,, Josef (referee) ; Vlček, Milan (advisor)
Topic of this dissertation thesis follows previous dissertations dealing with reconstructions of historical buildings that were successfully defended at Institute of Building Structures, Faculty of Civil Engineering, Brno University of Technology. The thesis deals with Romanesque and PreRomanesque round churches, called rotundas, that were built between 9th and 13th century in the historical territory of Great Moravia. Churches of similar shape can be also found in surrounding countries, but only scarcely. By the time of origin these rotundas were among the oldest masonry buildings built within borders of contemporary Czech Republic. Later some rotundas were destroyed and are known only thanks to the archaeological findings or written records. Some are still waiting to be discovered. Surviving rotundas are the oldest masonry buildings in Czech Republic, therefore it can be said that they belong to the most valuable historical buildings in the country. Preserved rotundas were often modified or rebuild in some way. Thanks to their age, origins of many of these buildings are shrouded in a mystery, which is one of the reasons why they attract attention of many researchers – archaeologists, historians and art historians. Many questions arise from their research. These questions have interdisciplinary character and finding the answers requires cooperation of specialists in different fields. One of these fields is building engineering. This dissertation thesis deals with proportional and structural analysis of PreRomanesque and Romanesque rotundas. For the proportional analysis author focused on verifying of some of the hypotheses of other researchers connected to the Romanesque rotundas. These include hypothesis dealing with use of historical units for the design of rotundas, hypothetical use of proportional canon, or some universal sets of proportional ratios of vertical and horizontal dimensions. The proportional analysis also helped with verification of some hypothe


Investment Project Management
Koukal, Marek ; Kříž, Pavel (referee) ; Waldhans, Miloš (advisor)
The diploma thesis is focused on evaluation of efficiency and feasibility of the project. In the theoretical part, there are described extensive issues of feasibility study. The thesis deals with evaluation of project effectiveness and its risks. The practical part analyzes the current unsatisfactory condition of a particular building. There are designed and processed two alternative solutions of the project including their evaluation. These solutions were compared with each other and presented to the investor.


Design of transport mechanism for the stationary robot
Kříž, Pavel ; Vejlupek, Josef (referee) ; Ripel, Tomáš (advisor)
This bachelor's thesis describes design of the transport mechanism for the autonomous robot. The main aim is modification of the chassis and design of the control mechanism. The designed concept comes out of requirements assigned by external company. It also includes the list and description of various considered concepts. The final construction variant is divided into several construction sections described in the thesis. The check calculation of potentially critical part is specified in the final part. The result is design of the transport mechanism for the stationary robot which serves as multifunctional kiosk.


Using thermoelectric generator to increase the efficiency of the radiator
Kříž, Pavel ; Janák, Luděk (referee) ; Vlach, Radek (advisor)
This diploma thesis deals with a design layout of the fan power supply that ensures the increase of the efficiency of the heating unit. For usage in the areas without electric power, the power supply is secured by thermoelectric generator. The system has to function on the basis of autonomous system which turns itself on only when necessary. In the introductory part of the paper there is a recherché of thermoelectric generators for general usage. Next it mentions the basic findings in from the field of DC/DC converters for low power applications. In this part attention is given to MPPT algorithm. Furthermore basic knowledge from the field of heat transmission together with its most used elements is described. Subsequently existing applications that increase the effectiveness of heating are mentioned. Their disadvantage however is that they depend on the external source of power supply. The practical part to a large extent covers the analysis of the suitability of the chosen thermoelectric module. For securing of the heat gradient of the generator there was a model created meeting the figures in the manual and there are several simulations in the MATLAB program. Furthermore several measurements of the thermoelectric module took place in order to secure realistic figures. Subsequently a DC/DC converter was chosen. Finally the testing was made on the real composition. In conclusion there is an overall evaluation including the real usage and the economical aspect of the project. The outcomes of the work enable to avoid common mistakes that are part of many specialized articles. The created system is to be used after the adjustment of the cooling to the required aim. At the same time it becomes very effective.


Likelihood based estimation
Březinová, Eva ; Maciak, Matúš (advisor) ; Kříž, Pavel (referee)
In this thesis we will describe the maximum likelihood method, method of estima ting unknown parameters that determine the probability distribution of the observed data. We will also introduce other methods derived from the likelihood. We focus pri marily on a quasilikelihood and a pseudolikelihood approach. Then we briefly describe profile likelihood, empirical likelihood, and conditional likelihood. The thesis includes a simulation study which compares the quality of the estimators based on the maximum likelihood and the quasilikelihood or the maximum likelihood and the pseudolikelihood using the mean squared error. 1


Approximations of the Aggregate Loss Distribution
Antalicová, Viktória ; Mazurová, Lucie (advisor) ; Kříž, Pavel (referee)
This thesis is focused on the approximation of the distribution of aggregate losses. We first present a method for modelling aggregate losses, which involves selecting an appropriate frequency and severity distributions. Next, the computation of aggregate losses as the sum of the respective number of individual losses is explained. In the sec ond section, we discuss the approximation of the distribution of the simulated aggregate losses. We present the distributions chosen for the approximation, the method for esti mating the parameters of these distributions, and the subsequent testing of fit of these distributions with the actual distribution of the simulated aggregate losses. In the third chapter we show the results of this approximation and indicate the suitability of using each of the considered distributions for modelling aggregate losses. In the last section, we introduce the Edgeworth approximation as a method for approximating the distribution of aggregate losses. 1
