
Credit Derivatives Valuation
Promer, Marek ; Franěk, Petr (advisor) ; Dupačová, Jitka (referee)
Credit risk plays an important role in the pricing of financial instruments. In effort to avoid the dangers resulting from this risk were developed new financial instruments called credit derivatives. In this work, the main features of three types of credit derivatives are discussed: credit default swap, total return swap and credit linked note. Regarding to the major portion of credit default swap on the credit derivatives market, the work deals with the valuation of this exact instrument with three models for valuing a credit default swap. These models estimate the value of credit default swap, under which the premium required from one participant of the contract is meant.


ValueatRisk estimation  non standard approaches.
Picková, Radka ; Dupačová, Jitka (advisor) ; Šmíd, Martin (referee)
The topic of the presented work is ValueatRisk (VaR) and its estimation. VaR is a financial risk measure and is defined as a quantile of the distribution of future returns, resp. losses. There exist various methods based on different assumptions how to estimate VaR. The most commonly used methods usually assume that the returns, resp. losses, are independently and identically distributed, especially that they are normally distributed. Since this assumption is not satisfied for most daily financial data, many alternative approaches have been suggested to estimate VaR. In the presented work two of them are discussed in detail, the CAViaR method and its asymptotic properties and the method of filtered historical simulation. One part of the work are numerical experiments with real data.


Expected value of information in stochastic programming
Čížková, Jitka ; Dupačová, Jitka (advisor) ; Lachout, Petr (referee)
Stochastic problems (both twostage 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.


Multicriterial Optimization Problems with a Random Element and Stochastic Programming
Líkař, Jan ; Kaňková, Vlasta (advisor) ; Dupačová, Jitka (referee)
In practice we often have to solve optimization problems with several criteria. These problems are called multicriteria optimization problems. Such problems are presented in this thesis. It is important, whether parameters take unknown values at the moment of making decision. If these parameters are random variables, resulting problem is called stochastic multiobjective problem, otherwise it is called deterministic multiobjective problem. We describe how to choose some "good" solutions of deterministic problem. We investigate their relations as well. In the stochastic case we have to convert such problem to deterministic one. We introduce some possibilities how to do it. Then we are able to solve the problem. These concepts are demonstrated using examples. We present a numerical illustration as well (the Portfolio Selection problem).

 

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)


The transportation problem, its generalizations and applications in probability and statistics
Doležel, Pavel ; Dupačová, Jitka (advisor) ; Kopa, Miloš (referee)
Author describes a specific optimization problemthe transportation problem and analyzes relevant solution methods. Several methods of solving the transportation problem are listed, applied or introduced and applications of the transportation poblem in the theory of probability and mathematical statistics are presented, namely the statistical sorting in L1 norm and reconstruction of contingency tables. Special interest is devoted to several modifications of ordinary transportation problem, mainly the multiindex transportation problem. The crucial part of the work are selected applications of the transportation problem to particular problems and showing some algorithms used for finding solutions.


Multiobjective portfolio optimization
Malá, Alena ; Kopa, Miloš (advisor) ; Dupačová, Jitka (referee)
The goal of this thesis is to summarize three basic principles of solving multiobjective programming problems. We focus on three approaches: a linear combination of objective functions, εconstrained approach and a goal programming. All these methods are subsequently applied to US data. We consider monthly excess returns of ten US representative portfolios based on individual stock market capitalization of equity that serve as basic assets. Our aim is to find the efficient portfolios. Next we investigate a structure of these portfolios and their mutual relationships. Graphic representation of efficient frontiers is also included in the thesis. All calculations were performed using Mathematica software version 8.

 

Economic applications of geometric programming
Štěpánek, Ladislav ; Dupačová, Jitka (advisor) ; Zimmermann, Karel (referee)
Geometric programming is a special case of nonlinear programming, where objective function and constraints are shaped as posynomials. In this work we introduce geometric programming and solving methods. In~last chapter we will apply the geometric programming to CobbDouglas production function, create a model with random demand and possible extensions of this model. Powered by TCPDF (www.tcpdf.org)
