5,413 research outputs found
Náhodné procesy v analýze spolehlivosti
Get PDFNázev práce: Náhodné procesy v analýze spolehlivosti Autor: Kamil Chovanec Katedra: Katedra pravděpodobnosti a matematické statistiky Vedoucí diplomové práce: Doc. Petr Volf, CSc. e-mail vedoucího: [email protected] Abstrakt: Práce je zaměřena na analýzu spolehlivosti se zvláštním důrazem na Aalenův aditivní model. Při testování hypotéz v analýze spolehlivosti často získáváme proces, který za platnosti hypotézy konverguje ke Gaus- sovskému martingalu, jehož rozptyl umíme odhadnout rovnoměrně konzis- tentním odhadem. Dostáváme se tak vlastně k nové hypotéze o procesu získaném testováním původní hypotézy. Existuje více způsobů, jak tuto hy- potézu testovat. V práci jsou představeny některé z nich a síla těchto testů je pomocí Monte Carlo simulací porovnána pro různé modely a velikosti výběrového souboru. Ve speciálním případě je odvozen bod, který maxima- lizuje asymptotickou sílu dvou testů. Klíčová slova: Martingal, Aalenův aditivní model, riziková funkce 1Title: Random Processes in Reliability Analysis Author: Kamil Chovanec Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Supervisor's e-mail address: [email protected] Abstract: The thesis is aimed at the reliability analysis with special em- phasis at the Aalen additive model. The result of hypothesis testing in the reliability analysis is often a process that converges to a Gaussian martingale under the null hypothesis. We can estimate the variance of the martingale using a uniformly consistent estimator. The result of this estimation is a new hypothesis about the process resulting from the original hypothesis. There are several ways to test for this hypothesis. The thesis presents some of these tests and compares their power for various models and sample sizes using Monte Carlo simulations. In a special case we derive a point that maximizes the asymptotic power of two of the tests. Keywords: Martingale, Aalen's additive model, hazard function 1Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult
Random Processes in Reliability Analysis
No full textTitle: Random Processes in Reliability Analysis Author: Kamil Chovanec Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Supervisor's e-mail address: [email protected] Abstract: The thesis is aimed at the reliability analysis with special em- phasis at the Aalen additive model. The result of hypothesis testing in the reliability analysis is often a process that converges to a Gaussian martingale under the null hypothesis. We can estimate the variance of the martingale using a uniformly consistent estimator. The result of this estimation is a new hypothesis about the process resulting from the original hypothesis. There are several ways to test for this hypothesis. The thesis presents some of these tests and compares their power for various models and sample sizes using Monte Carlo simulations. In a special case we derive a point that maximizes the asymptotic power of two of the tests. Keywords: Martingale, Aalen's additive model, hazard function
Možnosti se stabilními distribucemi
No full textNázev práce: Možnosti se stabilními distribucemi. Autor: Andrea Karlová Katedra: Katedra pravděpodobnosti a matematické statistiky Vedoucí disertační práce: Doc. Petr Volf, CSc. Abstrakt: Stabilní rozdělení jsou úzce spojena s problematikou konvergence součtu nekonečných řad nezávislých náhodných veličin. Hustoty těchto pravděpodobnostních rozdělení jsou dobře zkoumána za použití integralních transformací. Nejprve shrneme známé výsledky odvozené pomocí Fourierovi transformace, dále se zaměříme na méně častou Mellinovu transformaci. Pomocí této budeme vyšetřovat rozdělení součinu dvou nezávislých stabilních náhodných veličin. Ve čtvrté kapitole zobecníme model Louise Bacheliera za pomoci stabilních rozdělení a budeme diskutovat prak- tické aspekty spojené s finančními deriváty. Klíčová slova: stabilní rozdělení, Mellinova transformace, součin nezávislých náhodných veličin, levy model, samoshodné plochy implikovaných volatilit 1Title: Options under Stable Laws. Author: Andrea Karlová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Abstract: Stable laws play a central role in the convergence problems of sums of independent random variables. In general, densities of stable laws are represented by special functions, and expressions via elementary functions are known only for a very few special cases. The convenient tool for investigating the properties of stable laws is provided by integral transformations. In particular, the Fourier transform and Mellin transform are greatly useful methods. We first discuss the Fourier transform and we give overview on the known results. Next we consider the Mellin transform and its applicability on the problem of the product of two independent random variables. We establish the density of the product of two independent stable random variables, discuss the properties of this product den- sity and give its representation in terms of power series and Fox's H-functions. The fourth chapter of this thesis is focused on the application of stable laws into option pricing. In particular, we generalize the model introduced by Louise Bachelier into stable laws. We establish the option pricing formulas under this model, which we refer to as the Lévy Flight...Matematicko-fyzikální fakultaFaculty of Mathematics and Physic
Options under Stable Laws
No full textTitle: Options under Stable Laws. Author: Andrea Karlová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Abstract: Stable laws play a central role in the convergence problems of sums of independent random variables. In general, densities of stable laws are represented by special functions, and expressions via elementary functions are known only for a very few special cases. The convenient tool for investigating the properties of stable laws is provided by integral transformations. In particular, the Fourier transform and Mellin transform are greatly useful methods. We first discuss the Fourier transform and we give overview on the known results. Next we consider the Mellin transform and its applicability on the problem of the product of two independent random variables. We establish the density of the product of two independent stable random variables, discuss the properties of this product den- sity and give its representation in terms of power series and Fox's H-functions. The fourth chapter of this thesis is focused on the application of stable laws into option pricing. In particular, we generalize the model introduced by Louise Bachelier into stable laws. We establish the option pricing formulas under this model, which we refer to as the Lévy Flight..
Petr Simon (1944-2018)
No full textThis article is a reflection on the mathematical legacy of Professor Petr Simon.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Analysi
Regresní modely v analýze přežití a spolehlivosti
No full textRegression models in survival analysis and reliability Doctoral thesis Petr Novák Charles University in Prague, Faculty of Mathematics and Physics Abstract: In present work we study methods for modeling the dependence of data from sur- vival and reliability setting on available explanatory variables. The first part of the work compares the properties of the Cox proportional hazards model, Aalen additive model and the Accelerated failure model for survival data. We present methods for testing goodness-of-fit based on counting processes and martingale theory, allowing to identify which model fits the data best. The second part focuses on modeling the lifetime of repairable systems. We study the means of incorporating the history of studied devices into the models, including the influence of corrective repairs and preventive maintenance actions. We demonstrate the introduced methods on real applications and study their properties in various situations on simulated data. 1Regresní modely v analýze přežití a spolehlivosti Disertační práce Petr Novák Univerzita Karlova v Praze, Matematicko-fyzikální fakulta Abstrakt: V předložené práci studujeme metody pro modelování závislosti dat z oblasti analýzy přežití a spolehlivosti na dostupných vysvětlujících proměnných. V první části práce studujeme základní modely analýzy přežití, porovnáváme vlastnosti Coxova modelu proporcionálního rizika, Aalenova aditivního modelu a modelu zrychleného času. Uvádíme metody pro testování dobré shody modelu s daty, založené na teorii čítacích procesů a martingalů, umožňující rozpoznat, který model popisuje data nejlépe. Druhá část se věnuje modelování opravitelných systémů. Studujeme způsoby, jak do modelů zahrnout informace o historii zařízení, včetně vlivu oprav a preventivní údržby. Užití představených metod předvádíme na příkladech z praxe a na simulo- vaných datech zkoumáme jejich chování v různých situacích. 1Katedra pravděpodobnosti a matematické statistikyDepartment of Probability and Mathematical StatisticsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult
Regression models in survival analysis and reliability
No full textRegression models in survival analysis and reliability Doctoral thesis Petr Novák Charles University in Prague, Faculty of Mathematics and Physics Abstract: In present work we study methods for modeling the dependence of data from sur- vival and reliability setting on available explanatory variables. The first part of the work compares the properties of the Cox proportional hazards model, Aalen additive model and the Accelerated failure model for survival data. We present methods for testing goodness-of-fit based on counting processes and martingale theory, allowing to identify which model fits the data best. The second part focuses on modeling the lifetime of repairable systems. We study the means of incorporating the history of studied devices into the models, including the influence of corrective repairs and preventive maintenance actions. We demonstrate the introduced methods on real applications and study their properties in various situations on simulated data.
Centralization of treasury management 2010
Get PDFThe book consists of five parts: 1. Treasury management and its responsibilities (Chapter 1‐4); 2. Decentralized treasury (Chapter 5); 3. Different phases of the centralization (Chapter 6‐9); 4. Outsourcing (Chapter 10) 5. Regional treasury centres (Chapter 11); 6. Best practices in a bank (Chapter 12); In the first part, the author describes the treasury management focusing on its three core responsibilities, such as assets and liabilities management, cash management, and financial risk management. The second part zooms in on decentralized treasury and decisions about the appropriate degree of centralization/decentralization of the treasury activities. Then we focus on the different phases of the process of centralization, from central interest rate and foreign exchange management through centralization of cash and liquidity management, then transaction processing up to fully centralized treasury. In part four we continue by discussing outsourcing as the next stage following centralization to achieve additional economic benefits. The fifth part contains especially a number of the location criteria, both tax and non‐tax, that must be evaluated during consideration where to establish the regional treasury centre. The last part deals with banking best practices in cash pooling from the point of view of the author that works in one of the top banks in Central and Eastern Europe region
Cyclometalation of phenylpyridines with a ferrocenyl group
Get PDFNázev práce: Cyklometalace fenylpyridinů s ferrocenylovým substituentem Autor: Bc. Petr Harmach Katedra: Katedra anorganické chemie Vedoucí diplomové práce: prof. RNDr. Petr Štěpnička, Ph.D., DSc. Abstrakt: Cílem této práce byla příprava cyklometalovaných komplexů fenylpyridinů s ferrocenylovým substituentem. Cyklometalované komplexy mají široké spektrum využití, kdy jedním z nejvýznamnějších je použití v katalýze. Připraveny byly iridité a rhodité cyklometalované komplexy s elektrondonorními nebo elektronakceptorními skupinami na pyridinovém kruhu. Všechny tyto látky byly charakterizovány 1 H a 13 C{1 H} NMR spektroskopií, hmotnostní spektrometrií, elementární analýzou a cyklickou voltametrií. U dvou připravených látek byly jejich struktury potvrzeny pomocí metody difrakce rentgenového záření na monokrystalech. Klíčová slova: cyklometalace, pyridin, C-H aktivace, ferrocenTitle: Cyclometalation of phenylpyridines with a ferrocenyl group Author: Bc. Petr Harmach Department: Katedra anorganické chemie Supervisor: prof. RNDr. Petr Štěpnička, Ph.D., DSc. Abstract: The objective of this thesis was the synthesis of cyclometalated complexes of phenylpyridine with a ferrocenyl group. Cyclometalated complexes have a wide range of application, where one of the most important is the use in catalysis. Iridium(III) and rhodium(III) cyclometalated complexes were prepared containing electron-donating or electron-accepting groups on the pyridine ring. All newly prepared complexes were characterized by 1 H a 13 C{1 H} NMR spectroscopy, mass spectrometry, elemetal analysis and cyclic voltammetry. The structures of two complexes were determined by single-crystal X-ray diffraction analysis. Key words: cyclometalation, pyridine, C-H activation, ferroceneDepartment of Inorganic ChemistryKatedra anorganické chemiePřírodovědecká fakultaFaculty of Scienc
Jubilees and news
No full textsummary:Netuka, Ivan; Veselý, Jiří: Sedmdesátiny profesora Jana Maříka.
Volf, Ivo: 21. mezinárodní fyzikální olympiáda.
Volf, Petr: Tradice pražské konference o teorii informace pokračuje
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