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Econometric models for Czech insurance market
Vichr, Jaroslav ; Cipra, Tomáš (advisor) ; Pešta, Michal (referee)
Relationships between insurance variables representing the cash flows of the Czech insurance market can be effectively modeled using a dynamic system of linear simultaneous equations. The source of the underlying data to build such a model can be publicly available annual reports of the Czech Insurance Association. The resulting model can find its use mainly to predict the future development of financial flows based on historical observations and analysis of possible scenarios. It is this analysis of potential projections and their consequences which provides insight into how e.g. a future decrease of new insurance policies would affect the expected amount of claims costs and the volume of written premiums.
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Claims reserving within the panel data framework
Gerthofer, Michal ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
In the presented thesis the issue of dependency between response variables within the subjects in the generalized linear models framework is investigated. Reserving in non-life insurance is a key factor for the financial position of a company. The text introduces the basic actuarial notation, terminology and methods. The main part is focused on panel data framework, especially Generalized Linear Mixed Models (GLMM) as well as Generalized Estimating Equations (GEE), and their application on claims reserving. The aim of this thesis is to show the advantages, disadvantages, limitations and the comparison of these approaches on representative datasets, which were chosen according to results obtained from whole database analysis. Significant focus is on model selection and diagnostics used for this purpose. Finally, the obtained results are summarized in tables, figures and the comparison of the methods is provided. Powered by TCPDF (www.tcpdf.org)
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Generalized Leontiev models
Hála, Petr ; Kopa, Miloš (advisor) ; Cipra, Tomáš (referee)
"his thesis de-ls with veontiev¡s input -nd output model of the e onomy -nd its potenti-l extensionsF et the eginning of the thesis -si formul-tions -nd h-r- teristi s of the veontiev¡s model -re summ-rized with emph-sis on its solv- ilityF sn the third -nd fourth h-pterD we present the simplest modi( -tions with -ddition-l restri tions or o je tive fun tionF sn the sixth h-pter - dyn-mi model with dis rete time is derivedD -g-in with emph-sis on the formul-tion of the onditions of existen e of solutionF "he l-st h-pter presents - sto h-sti gener-liz-tion of the veontiev¡s model using pro - ilisti onstr-ints -nd the s en-rio -ppro- hF "he thesis is - omp-nied y its own ex-mple of veontiev¡s sto h-sti modelF
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Methods for periodic and irregular time series
Hanzák, Tomáš ; Cipra, Tomáš (advisor) ; Arlt, Josef (referee) ; Prášková, Zuzana (referee)
Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity
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Pensions from the point of view of utility theory
Kudlík, Michal ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This work deals with pensions from the perspective of utility theory. We list several basic principles, characteristics of pensions and their classification. Part of the work is also the utility theory from the ordinal point of view of utility theory as well as in terms of cardinal utility functions. Afterwards, we formulate the tasks for the selected utility functions, which we will try to optimize by using utility functions. We transfer the task of maximizing objective function to the task with extreme bound corresponding to various annuity markets which we will solve by theory of Lagrange multipliers. Final result of the work should be calculation of annuity equivalent wealth per common utility function Constant relative risk aversion (CRRA) using different relative risk aversions and showing the optimum consumption strategy for pensioners calculated based on mortality tables for Czech republic from 2012. 1
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Seasonal state space modeling
Suk, Luboš ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
State space modeling represents a statistical framework for exponential smoo- thing methods and it is often used in time series modeling. This thesis descri- bes seasonal innovations state space models and focuses on recently suggested TBATS model. This model includes Box-Cox transformation, ARMA model for residuals and trigonometric representation of seasonality and it was designed to handle a broad spectrum of time series with complex types of seasonality inclu- ding multiple seasonality, high frequency of data, non-integer periods of seasonal components, and dual-calendar effects. The estimation of the parameters based on maximum likelihood and trigonometric representation of seasonality greatly reduce computational burden in this model. The universatility of TBATS model is demonstrated by four real data time series.
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Credibility models for claim frequency
Biolek, Jiří ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
The work deals with estimation of unknown risk parameters of a driver. Risk parameter indicates how many times more accidents we may expect from this driver compared with the average insurance group to which the driver is assigned according to the precarious classification. Risk parameter is a random variable, which is depending on the damage share of this driver. The second and third chapters describe the derivation of the estimates that minimize the quadratic and exponential loss function. It also compares the level of these estimates and the convergence rate. In chapter four there are several simulations performed and tables with estimates for any specific data created. 1
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Numerical study on simultanious equations
Šaroch, Vojtěch ; Lachout, Petr (advisor) ; Cipra, Tomáš (referee)
Title: Numerical study on simultanious equations Author: Vojtěch Šaroch Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Petr Lachout, CSc. Abstract: In this thesis we deal with the simultaneous equation model. In the first chapter we introduce theoretical aspect of this problem, especially estimation procedures and their properties. We mention issues of an identification and an inconsistency of OLS-estimates for simultaneous modeling. In th second chapter we introduce theory of estimation, especially we will focus on the interval estimation and precision. We mention empirical approach too. In the third chapter we perform a numerical study on the simple macroeconomic model of generated dates. We are interested in properties of interval estimations of parameters, the convergence rate, difference between the empirical and theoretical extimation etc. Keywords: simultaneous equations model, interval estimation, empirical estimation 1
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Time series models with exogenous variables and their application to economical data
Vaverová, Jana ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
This thesis deals with analyzing multivariate financial and economical data. The first section describes the theory of multivariate time series and multivariate ARMA models. The second part deals with some models with exogenous variables such as simultaneous equations models and ARMAX model. In the final chapter, the described theory is applied to analyze the reciprocal dependence of time series of inflation rates and dependence of inflation rates on various macroeconomical indicators. The results were obtained by software Mathematica 8, Mathematica 10, EViews and R. Powered by TCPDF (www.tcpdf.org)
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Holt-Winters method for exponential smoothing
Koritarová, Lenka ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
"his thesis de-ls with the methods of exponenti-l smoothingF et (rst the prin iE ples of exponenti-l smoothing -re expl-inedF e fo us on -si -ppro- hesX sinE gleD dou le smoothing -nd the rolt¡s methodF "hese pro edures -re suit- le for the modeling time series without se-son-l omponentF rowever in pr- ti e there -re frequent time series with se-son-lityF por su h time series the roltE inter¡s method is usedF "his method is -sed just on the prin iples of exponenti-l smooE thingF sn the l-st p-rt of this thesisD there is demonstr-ted using this methods on re-l d-t-F
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