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Properties of the utility function in methods of MCDM
KADLEC, Josef
This thesis was concetrated on the value of utility function properties in the application of multi-criteria variance estimation models. The aim was to identify the deficiencies in the current utility function and to find the optimal alternative. Our study is based on the analysis of a case example involving the selection of an apartment for a student seeking accommodation. The relevance of different features of the utility function and their influence on the overall evaluation and decision making was investigated. Analytical methods and models were used to quantify this issue. The thesis was concluded by discussing the impact of identified utility function deficiencies on the evaluation results and suggesting a more appropriate utility function for multi-criteria variant evaluation applications. This study was sought to contribute to a better understanding of the influence of utility function characteristics on the quality of evaluation and decision making in multi-criteria analysis.
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Utility function in the decision-making process
MARÝŠKA, Patrik
This diploma thesis deals with the process of creating an application with appropriate alghoritms and mechanisms for constructing utility function for money for a given decision maker. Related theoretical topics from the decision theory, utility theory and especially the process of construction of the utility function for money are explained. Application randomly generates questions in given intervals for the decision maker. After the process of the generating question is finished, alghorithm for finding optimal starting values is applied. This alghoritm gradually compares SSE in the calculated interval. Nonlinear regression is used to fit the data gathered in previous steps. The graph of the found utility function is drawn and found parameters of the utility function are displayed together with the corresponding data. The paper goes on to evaluate the functionality of the application by solving model examples (St.Petersburg paradox, Powerball lottery and Cube lottery) for two different decision makers. These decision makers used designed application for constructing their utility functions for money. These two utility functions are utilized for calculating certainty equivalents for both decision makers and the results are compared. Application is implemented in Python and PyQt5.
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Optimal trading and pricing of financial derivatives
Samek, Daniel ; Dostál, Petr (advisor) ; Hlubinka, Daniel (referee)
In the text of this thesis we deal with the task of valuing financial derivatives. The theory is based on the Douglas theorem and its financial interpretation upon which we state replication theorem. These theorems connect martingale measures and existence of no-arbitrage price of derivative in both discrete and continuous time. Next part discusses trading strategies maximizing expected utility and their impact on existence of martingale measure. In the last chapter there are stated fundamental theorems of asset pricing which sum up main previous results. Powered by TCPDF (www.tcpdf.org)
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Modeling of risk aversion
Navrátil, František ; Lachout, Petr (advisor) ; Kopa, Miloš (referee)
of the master thesis Title: Modeling of risk aversion Author: František Navrátil Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Petr Lachout, CSc. Abstract: The thesis discusses various theories that are able to model investor's subjective attitude to risk. The goal of the thesis is to clearly recapitulate possible mathematical approaches and to apply them in a real situation. One of the ways to tackle the problem is to use expected utility theory and a specific shape of a utility function. Another way is to choose a suitable risk measure. Especially useful for the modelling of risk aversion is the class of spectral risk measures that enables investor to choose a risk spectrum that meets his perception of risk. The thesis contains basic definitions concerning stochastic programming - a theory essential to solve the related optimization problems. Keywords: Risk aversion, utility function, probability constraint.
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Riešenie problému vzácnosti súkromných pozemkov v susedstve solárnych elektrární pomocou coasovského teorému
Joppek, Ľubomír
With the recent solar boom there is a problem of the protection zone power plants, because while in conventional power plants, the extent was not the big problem, with a massive deployment of solar power plants in the vicinity of dwellings there is a problem regarding the use of these lands. The problem is not in the Czech Republic standard solution and bachelor thesis offer the right innovation as a cost effective solution to the current situation. The first part analyses the emergence of the problem and compares its development to developments abroad. The subsequent section will deal with the genesis of the problem and the solution will subsequently be introduced by Law and Economics, where they compared two approaches to dealing with externalities. Solving the problem will be based on Coasean agreements and Pigouvian tax comparative to the current state.
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