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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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Fuzzy Preference Structures in Multicriterial Decision Making
Majer, Tomáš ; Stryka, Lukáš (referee) ; Hliněná, Dana (advisor)
V mnohých rozhodovacích problémech evaluujeme akce z různých pohledů, které nazýváme kritéria. Například při ohodnocovaní auta uvažujeme kritéria jako maximální rychlost, cena, zrychlení a spotřeba. V obecnosti při rozhodování s ohledem na různá kritéria se setkáváme s problémem preferencí. Jedním z nejjednodušších řešení je vážený průměr uvažovaných kritérií. V této práci aplikujeme výsledky řešení jednoho multiriteriálního problému, přičemž porovnávání kritérií realizujeme použitím fuzzy preferenčních struktur. Naše řešení je ilustrováno na praktickém příkladě.
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FOREST ECOSYSTEM SERVICES: SELECTED KNOWLEDGE
Melichar, J. ; Horváthová, Eva
The assessment of ecosystem services (ES) has become an important concept during the last two decades and a model tool used to quantify the contribution of individual ecosystems (including the global one)\nand biodiversity to human well-being. Although there are a number of conceptual frameworks and a wide variety empirical applications, there is a lack of more detailed theoretical definitions based on ecological and economic theories as well ambiguity persists in defining the term ecosystem service. Ad hoc delineation and general formulation of this the concept is then limiting in the interpretation of the achieved results, the possibility of comparison across studies, including implementation transfer of values and functions of values, or when designing economic instruments such as payments for ecosystem services. Therefore, in this paper we discuss terms such as final product, intermediate product,\necological production function and utility function, i.e. concepts that are decisive for the correct definition of ES from the point of view economic theory.
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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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Suitable utility function identification
Majerová, Michaela ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
At the beginning of this work we study basic properties of utility functions and connection between their shape and investor's relation to risk. Then we define risk premium and we recall measure of risk aversion. In the second chapter we study classification of utility functions according to the absolute risk aversion measure and we list some basic types of utility functions. In the third chapter we construct investor's utility function. We use values of insurance premium which we get from questionnaire filled by MFF UK students. We use these utility functions in the last chapter. First we define portfolio selection problem and then we find optimal portfolio for different investors.
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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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Suitable utility function identification
Majerová, Michaela ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
At the beginning of this work we study basic properties of utility functions and connection between their shape and investor's relation to risk. Then we define risk premium and we recall measure of risk aversion. In the second chapter we study classification of utility functions according to the absolute risk aversion measure and we list some basic types of utility functions. In the third chapter we construct investor's utility function. We use values of insurance premium which we get from questionnaire filled by MFF UK students. We use these utility functions in the last chapter. First we define portfolio selection problem and then we find optimal portfolio for different investors.
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Paradoxes in Probability Theory
Rušin, Ján ; Haman, Jiří (advisor) ; Dostál, Petr (referee)
The Bachelor's thesis present an overview and description of selected probability theory paradoxes, namely the paradox of Monty Hall, the Bertrand's paradox and the St. Peterburg paradox. In every chapter the reader is at first apprised of the formulation and the essence of the paradox. Then we show some possible solutions of this paradox. In original formulation of Monty Hall paradox there exists just one solution which can be reached by using two different ways. We add also some simple modifications to this particular paradox. The formula- tion of Bertrand's paradox is ambiguous which we show by using four selected approaches. And very similar situation arises in St. Peterburg paradox which we resolve by using three different approaches. 1
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Fuzzy Preference Structures in Multicriterial Decision Making
Majer, Tomáš ; Stryka, Lukáš (referee) ; Hliněná, Dana (advisor)
V mnohých rozhodovacích problémech evaluujeme akce z různých pohledů, které nazýváme kritéria. Například při ohodnocovaní auta uvažujeme kritéria jako maximální rychlost, cena, zrychlení a spotřeba. V obecnosti při rozhodování s ohledem na různá kritéria se setkáváme s problémem preferencí. Jedním z nejjednodušších řešení je vážený průměr uvažovaných kritérií. V této práci aplikujeme výsledky řešení jednoho multiriteriálního problému, přičemž porovnávání kritérií realizujeme použitím fuzzy preferenčních struktur. Naše řešení je ilustrováno na praktickém příkladě.
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