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Expected value of information in stochastic programming
Čížková, Jitka ; Dupačová, Jitka (advisor) ; Lachout, Petr (referee)
Stochastic problems (both two-stage and multistage) can be formulated in several di erent ways which utilize to various extent available information on a future realization of incorporated random parameters. When comparing optimal objective function values resulting from di erent formulations of the given problem with the same available information, we obtain a value of using one of these formulations rather than the other one (e.g., VSS). Level of the available information can be changed by a partial or full relaxation of nonanticipativity constraints, which assure that a present decision is independent of future (unknown) realizations of random parameters. By comparing optimal objective function values gained when solving the given problem with distinct levels of available information we obtain (expected) value of partial or perfect information. In this work we present de nitions of various information value types and related values connected with the problem formulation and we derive their properties (nonnegativity, bounds). In the last part we introduce their summary classi cation.
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Dynamic fare model
Kislinger, Jan ; Lachout, Petr (advisor) ; Hlubinka, Daniel (referee)
The problem of creating dynamic fare model consists of two tasks - estimating demand for train tickets and multistage optimization of price of fare. We introduce a model of inhomogeneous Markov process for the process of selling the tickets in this thesis. Because of the complexity of the state space the optimization problem needs to be solved using simulation methods. The solution was implemented in R language for single-stage and two-stage problems. Before this application we summarize the theory of inhomogeneous Markov process with special attention to process with separable inhomogeneity. Then we propose methods for estimating the intensity using maximum likelihood theory. We also describe and compare two algorithms for simulated optimization. Powered by TCPDF (www.tcpdf.org)
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Modelování hry tenis
Tsapparellas, Kyriakos ; Lachout, Petr (advisor) ; Nagy, Stanislav (referee)
This thesis introduces three methods/models in forecasting the winner of a tennis match, analyzes them, studies their effectiveness under certain circumstances and detects their advantages or disadvantages using sufficient amount of previous data and results. Moreover, a personal fourth model is being introduced and tested which aims to give an answer to a question posted by Franc Klaassen and Jan Magnus, whether the forecast error can be reduced by not assuming that points during a match are independent and identically distributed and allows changes to happen as the match unfolds. If there is an actual improvement it will be showed and discussed subsequently.
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Multicriteria games
Tichá, Michaela ; Lachout, Petr (advisor) ; Kaňková, Vlasta (referee)
The concern of this thesis is to discuss different multicriteria games solution concepts. Multicriteria game is a special case from the game theory if the payoff function of at least one player is a vector and the player wants to maximize all the criteria at the same time. The thesis is divided into four chapters. In the first instance a few motivation examples are introduced. Subsequently the history of the multicriteria games is mentioned. The theoretical chapter follows. It contains five sections - introduction of new definitions; the structure of the set of equilibria for two person multicriteria games; searching equilibria points by the help of scalarization of the vector-valued function; introduction of ideal equilibria points and ways how to find them; the comparison of used methods. The last solution concept is demonstrated by the real example. Finally a theoretical chapter with new results is included. 1
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Volatility bursts and order book dynamics
Plačková, Jana ; Swart, Jan (advisor) ; Lachout, Petr (referee)
Title: Volatility bursts and order book dynamics Author: Jana Plačková Department: Department of Probability and Mathematical Statistics Supervisor: Dr. Jan M. Swart Supervisor's e-mail address: swart@utia.cas.cz Abstract: The presented paper studies the dynamics of supply and demand through the electronic order book. We describe and define the basic rules of the order book and its dynamics. We also define limit and market orders and describe the differences between them and how they influenced the evolution of ask, bid price and spread. Next part of the paper is dedicated to the de- scription and definition of volatility and its basic models. The brief overview about volatility clustering and its modeling by economists and physicists can be found in the following part. In the last part we introduce a simple model of order book in which we observe ask, bid price and spread. Then we study the empirical distribution of spread and try to find its probability distribu- tion. The volatility clustering is then observed through the relative returns of spread. In the last part we introduce some possible improvement of the model. Keywords: volatility clustering, order book, limit orders, market orders 1
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