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Contemporary measures of financial risk
Leder, Ondřej ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The main goal of this work is to talk about some financial risks and to introduce some methods of measuring them. The most important part of this work is the value at risk, its extension in form of conditional value at risk and introduction of some of its possible alternatives, which are expectile and spectral risk measures. For this it is needed to give a theoretical framework from the theory of probability. Its goal is to show the similarity of expectile and quantile, because value at risk is practicaly a quantile. Another goal of this fork is to show some weak properties of VaR and to practically illustrate the possibility of using expectile as an alternative to VaR. Powered by TCPDF (www.tcpdf.org)
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Fixed interval scheduling problems - stochastic extensions, formulations and algortihms
Leder, Ondřej ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
Fixed interval scheduling problems have wide range of practical use in production planning, transportation, in hospitals or in schools when planning timetables. When solving these problems we often encounter requirement of integrality of solutions. Ignoring this condition is often not possible. In this thesis we propose some formulations of scheduling problems and their stochastic extensions. We also propone a new formulation of stochastic FIS problem, for which integrality of solution is byproduct of its definition. We present Gâteaux derivative and its relationship to stability of optimal value function of stochastic optimization problems under the influence of contamination. We propose a new theorem on the stability of such functions for fixed interval scheduling problems.
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Fixed interval scheduling problems - stochastic extensions, formulations and algortihms
Leder, Ondřej ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
Fixed interval scheduling problems have wide range of practical use in production planning, transportation, in hospitals or in schools when planning timetables. When solving these problems we often encounter requirement of integrality of solutions. Ignoring this condition is often not possible. In this thesis we propose some formulations of scheduling problems and their stochastic extensions. We also propone a new formulation of stochastic FIS problem, for which integrality of solution is byproduct of its definition. We present Gâteaux derivative and its relationship to stability of optimal value function of stochastic optimization problems under the influence of contamination. We propose a new theorem on the stability of such functions for fixed interval scheduling problems.
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Contemporary measures of financial risk
Leder, Ondřej ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The main goal of this thesis is to talk about some financial risks and to introduce some methods of measuring them. We place great emphasis on the value at risk, its extension in form of conditional value at risk and introduction of some of its possible alternatives, which are expectile and spectral risk measures. For this it is necessary to introduce some findings of the theory of probability. Our goal is to show the similarity of expectile and quantile, because value at risk is practicaly a quantile. Another goal of this thesis is to show weakness of VaR and to practically illustrate the possibility of using expectile as an alternative to VaR. Powered by TCPDF (www.tcpdf.org)
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Contemporary measures of financial risk
Leder, Ondřej ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The main goal of this work is to talk about some financial risks and to introduce some methods of measuring them. The most important part of this work is the value at risk, its extension in form of conditional value at risk and introduction of some of its possible alternatives, which are expectile and spectral risk measures. For this it is needed to give a theoretical framework from the theory of probability. Its goal is to show the similarity of expectile and quantile, because value at risk is practicaly a quantile. Another goal of this fork is to show some weak properties of VaR and to practically illustrate the possibility of using expectile as an alternative to VaR. Powered by TCPDF (www.tcpdf.org)
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