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Stochastic DEA and dominance
Majerová, Michaela ; Kopa, Miloš (advisor) ; Dupačová, Jitka (referee)
At the beginning of this thesis we discuss DEA methods, which measure efficiency of Decision Making Units by comparing weighted inputs and outputs. First we describe basic DEA models without random inputs and outputs then stochastic DEA models which are derived from the deterministic ones. We describe more approaches to stochastic DEA models, for example using scenario approach or chance constrained programming problems. Another approach for measuring efficiency employs stochastic dominance. Stochastic dominance is a relation that allows to compare two random variables. We describe the first and second order stochastic dominance. First we consider pairwise stochastic efficiency, then we discuss the first and second order stochastic dominance portfolio efficiency. We describe different tests to measure this type of efficiency. At the end of this thesis we study efficiency of US stock portfolios using real historical data and we compare results obtained when using stochastic DEA models and stochastic dominance. Powered by TCPDF (www.tcpdf.org)
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Application of game theory on oligopoly structures
Kuzmiak, Maroš ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
This bachelor thesis is devoted to the games theory and its application to economic models of oligopolies. We focus on determining optimal strategies in non-cooperative conflict and on the issue of coalitions forming and rewards redistribution in cooperative conflict. Lessons learned and characteristics obtained are afterwards applied to different models of oligopolies. Individual chapters are supplemented by short numerical examples which are used to demonstrate the explained theory. The application of this work is to be found in areas where conflict situations are modeled using the knowledge on the choice of optimal strategies.
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Stochastic models in consumer theory
Vlčková, Ivona ; Kopa, Miloš (advisor) ; Dvořák, Marek (referee)
The goal of this bachelor's thesis is the stochastic extension of deterministic models with a special attention to finding the consumer's optimum. The first chapter is devoted to utility theory, defining basic notions and it also studies characteristics of utility functions and indifference curves. Futhermore, the consumer's optimum is described from the perspective of marginal utility. At the end of this chapter, optimization problems are provided, including their solutions, and finally we examine the effect of price changes of particular goods and income. This effect is described and solved via the substitution and income effect. The second chapter shows the stochastic extension of the above mentioned models. Using the quantile function, we obtain the optimum in the case of random income and we use mean values for the case of random prices. Eventually, a considerable part of this work is devoted to scenario theory, which is also used in the final example.
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Stochastic programming problems with chance constraints
Harcek, Milan ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
The thesis presents stochastic programming with chance contraints. We begin with the definition of convex set, convex and concave function and we study the convexity of programs with deterministic constraints. We continue with the definition of quasi-concave and quasi-convex function. After that, we put our mind to probabilistic constraints and the convexity of feasible set and show the formulation of joint and separate probabilistic constraints. We discuss properties of feasible set in general case, without any assumptions concerning the probability distribution of random variable. Finally, we apply our theory to random vectors with finite discrete distribution and multiva- riate normal distribution. 1
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Výpočet korelace v úvěrovém portfoliu a její vliv na celkové kreditní riziko portfolia
Pacovský, Matěj ; Kopa, Miloš (advisor) ; Dostál, Petr (referee)
In recent years many works employed the topic of the estimation of the asset value correlation from the portfolio of debtors and their properties. The results vary depending on the methods used or the data sets, on which the model was applied. The Master Thesis describes the methods of estimation of the asset value correlation from 5-year default performance of small and medium-sized enterprise (SME) debtors of Komercni Banka. Each method is firstly described in detail and then applied. Estimations of the asset value correlation are performed in rating and industrial homogeneous group. The conclusion contains a comparison of resulting capital with a former Basel correlation and the capital when our estimations of the asset correlation are used as a parameters. Powered by TCPDF (www.tcpdf.org)
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Robustness of the Markowitz portfolios
Petráš, Tomáš ; Dupačová, Jitka (advisor) ; Kopa, Miloš (referee)
This diploma thesis deals with the problem of portfolio optimization in relation to the mean vector and the variance matrix of yields. The emphasis is put on Mar- kowitz model. In the thesis there are explored some possibilities of robustification based on the used parametric set. Beside the classic formulation of the task our focus is also devoted to the cases in which short sales are not allowed. The core of the thesis constitutes of a simulation study that models the impact of errors in the estimation of the input parameters of Markowitz model. It takes into account different types of risk aversions and different approaches to modelling parameter perturbations . Therefore it specifies the hypothesis of the dominating influence of the mean vector estimate which is valid only for a risk lover. 1
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Regression models and their teaching
Rybář, Marian ; Staněk, Jakub (referee) ; Kopa, Miloš (referee)
Title: "Regression models and their teaching" Author: Mgr. Marian Rybář Department: Department of Mathematics Education Abstract: Regression models and their outputs have a huge utilization not only in the field of medicine, science and managerial decision-making but also in many other fields. From the math didactics point of view is a question of intelligible explanation of regression models to non- math students very topical and exploitable theme. The main problem is an understandable explanation of this topic to statistics schooling members with minimal math application. These people aren't usually math or technical branch alumni, but they use regression models in their work. This work tries to suggest simply and clearly explanation of regression models on particular examples. Practical examples show the effects of the most common mistakes that are made by laymen in application of regression models. The main output of this work is a set of examples that could be used in regression models schooling. Keywords: regression models, regression analysis, didactics, teaching
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