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Game Theory in Waste Management
Eryganov, Ivan ; Hoff, Arild (referee) ; Kopa, Miloš (referee) ; Hrdina, Jaroslav (advisor)
Teorie her se zabývá temáty, jako je spolupráce, konkurence a seberegulace v prostředí, kde je zapojeno mnoho entit s protichůdnými cíly. Rozdílné zájmy jsou běžné při řešení environmentální udržitelnosti a oběhového hospodářství. Tato Ph.D. práce je věnována aplikacím teorie her v odpadovém hospodářství s důrazem na energetické zpracování nerecyklovatelného odpadu. Po úvodu je shrnuto základní pozadí teorie her, které poskytuje přehled o součásném stávu poznání. Poté jsou přezkoumány novodobé aplikace metod teorie her v problematice udržitelnosti, aby se zdůraznila aktuálnost práce. V závěru je uveden vlastní přínos autora v aplikaci nekooperativních a kooperativních her v oblasti odpadového hospodářství. Konkretně je Ph.D. práce zaměřena na hru o stanovení cen zařízeními pro energetické využití odpadů a hru o minimalizaci nákladů producentů odpadů. Jsou podrobně studovány teoretické vlastnosti těchto her. Pro řešení uvažovaných her jsou navrženy originální algoritmy pro problémy dvouúrovňové optimalizace a vytváření dynamických koalic. Výsledky případových studií ukazují racionální vyústění konfliktů a dokazují, že navrhované přístupy k uvažovaným problémům odpadového hospodářství jsou rozumné.
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Expectiles and their estimates
Škurek, Jan ; Hudecová, Šárka (advisor) ; Kopa, Miloš (referee)
This bachelor's thesis focuses on studying expectiles as an alternative approach to traditional quantiles. Expectiles are becoming increasingly popular as risk measures in various fields, including finance and insurance sectors. The thesis presents basic properties and derivations of expectiles in detail. In addition to the definition of sample expectiles, a parametric estimation method for expectiles is introduced. The practical part is devoted to the estimation of sample expectiles, parametric estimation using the method of mo- ments, and a comparison of both methods on a simulated sample from the exponential distribution. 1
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Discrete sequential games with random payoffs
Račko, Lukáš ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
In our thesis we consider games with random payoff as a generalizations of the stan- dard concept of games in the game theory. We discuss possible optimality conditions for these types of games. In one of these approaches by the concept of a α-Nash equilibria we manage to prove the existence of this generalization of Nash equilibria for the case when the payoff has only finite number of realizations. We then apply those concepts to the case when the game is considered in multiple stages. In the practical part of this thesis we consider an application to a competition of internet providers which we model by a generalized version of the Cornout model of duopoly. We compare results of our optimal strategy with the deterministic approaches to this problem. 1
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Optimal choice of scenario tree using Reinforcement learning
Vondráček, Jakub ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multistage stochastic programs and explores the dependence of the obtained objective value on the chosen structure of the scenario tree. In particular, the scenario trees are built using the moment matching method, a multistage mean-CVaR model is formulated and a reinforcement learning agent is trained on a set of historical financial data to choose the best scenario tree structure for the mean-CVaR model. For this purpose, we implemented a custom reinforcement learning environment. Further an inclusion of a penalty term in the reward obtained by the agent is proposed to avoid scenario trees that are too complex. The reinforcement learning agent is then evaluated against an agent that chooses the scenario tree structure at random and outperforms the random agent. Further the structure of scenario trees chosen by the reinforcement learning agent is analyzed. 1
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Stochastic multistage problems for drug transportation
Tekulová, Paula ; Kopa, Miloš (advisor) ; Procházka, Vít (referee)
This thesis deals with the multi-stage stochastic problems for drug distribu- tion. In the first chapter, we introduced two-stage and multi-stage stochastic programming problems. In the second chapter, we constructed a scenario tree and introduced two methods on how to generate scenarios - the moment method and paths-based methods. In the third chapter, the transportation problem is formulated. Next, we introduced two-stage and multi-stage models, which aim to maximize the profit of pharmacies. The multi-stage models are then extended with probability constraints. In the practical part, we analyzed the historical data and eliminated the seasonality component. Then, we generated scenarios and constructed scenario trees. Lastly, we analyzed the results of the models. 1
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Asset-Liability Management:Application of Stochastic Programmingwith Endogenous Randomness andContamination
Rusý, Tomáš ; Kopa, Miloš (advisor) ; Consigli, Giorgio (referee) ; Branda, Martin (referee)
Title: Asset-Liability Management: Application of Stochastic Programming with Endogenous Randomness and Contamination Author: RNDr. Tomáš Rusý Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, PhD., Department of Probability and Mathematical Statistics Abstract: This thesis discusses a stochastic programming asset-liability management model that deals with decision-dependent randomness and a subsequent contamination analysis. The main model focuses on a pricing problem and the connected asset- liability management problem describing the typical life of a consumer loan. The endogeneity stems from the possibility of their customer rejecting the loan, the possibility of the customer defaulting on the loan and the possibility of prepay- ment which are all affected by the company's decision on interest rate of the loan. Another important factor, which plays a major role for liabilities, is the price of money in the market. There, we focus on the scenario generation procedure and develop a new calibration method for estimating the Hull-White model [Hull and White, 1990] under the real-world measure. We define the method for the gen- eral class of one-factor short-rate models and perform an extensive analysis to assess the estimation performance and...
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Spectral and distortion risk measures
Kočandrle, Erik ; Kopa, Miloš (advisor) ; Večeř, Jan (referee)
In this thesis we define risk measures as a way of quantifying the risk of an invest- ment and we formulate their essential properties, focusing mainly on coherency. Then we define the notions of admissible spectrum and spectral risk measures. Next we define the distortion function and distortion risk measures. We examine their core properties, relati- onships to coherency and formulate theorems describing their mutual equivalence with respect to the task of portfolio optimization. Lastly we tackle the problem of portfolio optimization on numerical data with respect to the MINVAR distortion function and its different values of the risk aversion parameter. 1
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Models for Forecasting Interest Rates with Application to Bond Portfolio Immunisation
Vaňková, Kateřina ; Kopa, Miloš (advisor) ; Večeř, Jan (referee)
Title: Models for Forecasting Interest Rates with Application to Bond Portfolio Immunisation Author: Kateřina Vaňková Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D., Department of Probability and Mathematical Statistics Abstract: The development and behaviour of interest rates play a crucial role in many financial fields. Interest rates can be forecasted using several models with different assumptions. In reality, these assumptions are not usually met. It leads to situations when a sophisticated and theoretically well-established model is not significantly better than simple methods, such as random walk. This thesis aims to study several approaches to interest rate forecasting, apply these approaches to European interest rate data, and find the best model for these real data. We will model European interest rates using several models. We will consider the Nelson- Siegel model (with two different approaches on how to estimate the shape parameter λ), the vector autoregression model with lag one (VAR(1)) and the Vasicek model. We will evaluate these models based on in-sample and also out-of-sample fit. We will use the Diebold-Mariano test to evaluate the statistical significance of models' forecast error differences. We select random walk as a benchmark...
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Optimization problems solving using various software
Petráš, Tomáš ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with practical problems when solving tasks of linear programming using mathematical software Mathematica, Gams, R and Matlab. It describes the basic properties of solvers, packages and optimizing functions of these programs. The aim of the thesis is to compare computer times needed to solve problems of different sizes using the considered programs. We consider these time efficiencies with and without the time consumed by loading the input data. At the end of the thesis we find the most suitable program for each of the problems sizes and we give some recomendations for the practical use of these products when solving problems of linear programming.
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Conic optimization: theory and applications
Dortová, Zuzana ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
1 This work discusses the roles of second-order cone programming, these tasks are a special class semidefinitního programming. The work summarized basic de- finitions, properties and claims known about these tasks. Special attention is paid to methods of solving SOCP problems. In the last part of the paper are formu- lated in some special tasks of mathematical programming (linear programming, quadratic programming, ...) as special cases of SOCP problems.
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