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Markov chains and credit risk theory
Cvrčková, Květa ; Prokešová, Michaela (advisor) ; Lachout, Petr (referee)
Markov chains have been widely used to the credit risk measurement in the last years. Using these chains we can model movements and distribution of clients within rating grades. However, various types of markov chains could be used. The goal of the theses is to present these types together with their advan- tages and disadvantages. We focus our attention primarily on various parameter estimation methods and hypotheses testing about the parameters. The theses should help the reader with a decision, which model of a markov chain and which method of estimation should be used for him observed data. We focus our attention primarily on the following models: a discrete-time markov chain, a continuous-time markov chain (we estimate based on continuous- time observations even discrete-time observations), moreover we present an even- tuality of using semi-markov chains and semiparametric multiplicative hazard model applied on transition intensities. We illustrate the presented methods on simulation experiments and simu- lation studies in the concluding part. Keywords: credit risk, markov chain, estimates in markov chains, probability of default 1
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Sekvenční metody Monte Carlo
Coufal, David ; Beneš, Viktor (advisor) ; Prokešová, Michaela (referee)
Title: Sequential Monte Carlo Methods Author: David Coufal Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Viktor Beneš, DrSc. Abstract: The thesis summarizes theoretical foundations of sequential Monte Carlo methods with a focus on the application in the area of particle filters; and basic results from the theory of nonparametric kernel density estimation. The summary creates the basis for investigation of application of kernel meth- ods for approximation of densities of distributions generated by particle filters. The main results of the work are the proof of convergence of kernel estimates to related theoretical densities and the specification of the development of approx- imation error with respect to time evolution of a filter. The work is completed by an experimental part demonstrating the work of presented algorithms by simulations in the MATLABR⃝ computational environment. Keywords: sequential Monte Carlo methods, particle filters, nonparametric kernel estimates
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Modelling Bonus - Malus Systems
Stroukalová, Marika ; Mazurová, Lucie (advisor) ; Prokešová, Michaela (referee)
Title: Modelling Bonus - Malus Systems Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., KPMS MFF UK Abstract: In this thesis we deal with bonus-malus tariff systems commonly used to adjust the a priori set premiums according to the individual claims during mo- tor third party liability insurance. The main aim of this thesis is to describe the standard model based on the Markov chain. For each bonus-malus class we also determine the relative premium ("relativity"). Another objective of this thesis is to find optimal values for the relativities taking into account the a priori set premiums. We apply the theoretical model based on the stationary distribu- tion of bonus-malus classes on real-world data and a particular real bonus-malus system used in the Czech Republic. The empirical part of this thesis compares the optimal and the real relativities and assesses the suitability of the chosen theoretical model for the particular bonus-malus system. Keywords: bonus-malus system, a priori segmentation, stationary distribution, relativity, quadratic loss function 1
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Comparison of Agonistic and Antagonistic Muscles Activity by Means of EMG by Different Implementation of Rhythmic Stabilization at Choice Facilitation Pattern
Chlupáčová, Veronika ; Holubářová, Jiřina (advisor) ; Prokešová, Michaela (referee)
Title: Comparison of agonistic and antagonistic muscles activity by Means of the EMG Implementation of different rhythmic stabilization at choice facilitation patty. Objective: using EMG measurements to compare the presence of symmetrical electrical activity Selected agonist and antagonist muscles of the upper limb at different how to perform rhythmic stabilization u! .diagonály HK Flexion PNF formula and determine method embodiment rhythmic stabilization, which is characterized by the presence of most symmetrical electromyographic activity of muscle we tested participating in the ~ above-mentioned movement pattern. Method: An experienced physical therapist conducted a 6 probands three ways to perform rhythmic stabilization and free kokontrakci without resistance at HK I. diagonal flexion formula from PNF during which the monitored electromyographic activity of selected agonistic and antagonistic muscles. The measured values are processed and compared. Our work is focused on the presence of symmetric muscle activity during rhythmic stabilization whether this affected sym.terie modus operandi rhythmic stabilization. Results: show that symmetrical muscle activity measured exhibits rhythmic stabilization when the resistance placed proximally agonists and simultaneously distally antagonists. Very similar...
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Third order moment characteristics for spatial point processes
Verchière, Didier ; Prokešová, Michaela (advisor) ; Pawlas, Zbyněk (referee)
Moment characteristics are widely used for the statistical analysis of spatial point processes. Standard summary statistics used for the analysis of point processes are of first and second order (intensity, K -function, pair-correlation function...). Nonetheless, none of these characteristics describes the distribution of a point pattern completely. Higher order characteristics such as third-order characteristics can give more information about the spatial interactions. Two such characteristics have already been studied: the z -function (Moller et. al. 98) and the T -function (Schladitz, Baddeley 2000). Key words: T -function, z -function , third order moment characteristics.
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Evalvation of Stereognostic Ability of Visually Handicapped group and group of Physiotherapists
Poubová, Jana ; Nováková, Tereza (advisor) ; Prokešová, Michaela (referee)
Abstraet: Evaluation ofstereognostic ability ofvisually handicapped group and group ofphysiotherapists Statements: We suppose that people with visual handicap will have a better tactile sensation as a compensation to worse visus. At the same time we suppose a better tactile sensation in a group of physiotherapists, beacause of a regular manual contact with patianťs body surface, which can help to improve tactile and proprioceptive sensation and also the stereognosis ability - differences in size, shape and surface without visual control. Our study is focused on testing of this ability in a group of visually handicapped people and a group ofphysiotherapists. Targets: To evaluate stereognosis in a group ofpeople with visual handicap, especially blind and weak-eyed people and a group ofphysiotherapists working with patiens S years in minimum. Methods: We determined three simple, not time demanding tests, which were used for testing in experim.ental our groups. Results: We found out better stereognostic ability in a group ofvisually handicapped people than in a group ofphysiotherapists. Conclusions: We proved better stereognostic ability in a group ofvisually handicapped people than in a group ofphysiotherapists. It woudl be good to make the same testing in nonnal population for supplementation, we would expect...
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Sequential Monte Carlo Methods
Sobková, Eva ; Zikmundová, Markéta (advisor) ; Prokešová, Michaela (referee)
Monte Carlo methods are used for stochastic systems simulations. Sequential Monte Carlo methods take advantage of the fact that observations are coming sequentially. This allows us to refine our estimate sequentially in time We introduce a State Space Model as a Hidden Markov Model. We describe Perfect Monte Carlo Sampling, Importance Sampling, Sequential Importance Sampling and discuss advantages and disadvantages of these methods. This discussion brings us to add a resampling step in Sequential Importance Sampling and introduce Particle Filter and Particle Marginal Metropolis-Hastings algorithm. We choose a Hidden Markov Model used for stochastic volatility modeling and make a simulation study in Wolfram Mathematica, version 8.
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