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Seasonal mortality and its application in life insurance
Srnáková, Andrea ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
Assumptions like uniform distribution, constant force of mortality and the Balducci assumption frequently used for modeling mortality data do not reflect the variability of monthly death rates. Often a phenomenon of winter excess mortality occurs, which is not respected by these assumptions. We shall apply a seasonal mortality assumption, which uses non-negative trigonometric sums for modeling the distribution of monthly death rates. We then apply our findings to the Czech mortality data. We calculate monthly premiums in a short-term life insurance policy and compare the result with results given by the classical assumptions. 1
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Claims reserve volatility and bootstrap with aplication on historical data with trend in claims development
Malíková, Kateřina ; Pešta, Michal (advisor) ; Zichová, Jitka (referee)
This thesis deals with the application of stochastic claims reserving methods to given data with some trends in claims development. It describes the chain ladder method and the generalized linear models as its stochastic framework. Some simple functions are suggested for smoothing the origin and development period coefficients from the estimated model. The extrapolation is also considered for estimation of the unobserved tail values. The residual bootstrap is used for the reparameterized model in order to get the predictive distribution of the estimated reserve together with its standard deviation as a measure of volatility. Solvency capital requirement in one year time horizon is also calculated. 1
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Risk aggregation allowing for skewness
Šimonová, Soňa ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
The main objective of this thesis is to examine different methods of calcula- tion of economic capital for an insurance company which allow for skewness. For calculating the economic capital we use two alternative risk measures- Value at Risk (VaR) and Conditional Value at Risk (CVaR). The first part of the thesis is concerned with deriving exact formulae for VaR and CVaR for normally distribu- ted losses and describing the modification of these formulae using Cornish-Fisher approximation. Next, the method using lognormal model with a parameter cap- turing skewness is discussed. The parameter is used for deriving a formula for skewness of a sum of losses. The approximation of the sum is thus obtained and is used for deriving formulae for VaR and CVaR for aggregated losses. Finally, the methods are compared numerically using R software. 1
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Parametric Nonlinearity Testing in Time Series
Kollárová, Dominika ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The aim of this bachelor thesis is the theoretical description of the functioning of two parametric nonlinearity tests - the RESET test and Keenan's test and theirs application on financial time series with the summary of achieved results. During the testing we assume, that a time series follows a predetermined linear AR(p) model the order of which is identified by the partial autocorrelation function or the AIC criterion.
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Composite distributions of loss sizes
Karatun, Ksenia ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
In this work, we deal with composite distributions that can be used to model loss sizes in some specific classes of non-life insurance. The first part contains definition of the general composite model and its special features. The second part describes models that are made up by piecing together Weibull distribution and distributions belonging to a family of transformed beta distributions. The third part describes algorithm that computes the maximum likelihood estimators for parameters of composite distribution and criteria of the relative quality of statistical models. In the last part we apply composite models to two real data sets. 1
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Linear and nonlinear autoregressive models for time series from economics and finance
Cvetković, Jelena ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
This bachelor thesis deals with linear and nonlinear autoregressive models for time series from economics and finance. It consists of theoretical and practical part. In theoretical part, the reader acquaints with terms connected to random proces- ses; then autoregressive and threshold autoregressive time series are introduced, their general properties are derived, possible ways of forecasting are described and ways of parameters estimation are presented. Furthermore, test for threshold autoregression is introduced. The practical part is divided into simulation study, where the quality of estimations and the power of the test is examined on simu- lated time series, and into application on real data, where the acquired findings are utilized on time series of share prices of the company ČEZ. 1
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Smooth Transition Autoregressive Models
Khýr, Miroslav ; Zichová, Jitka (advisor)
The aim of this work is describing theory of smooth transition autoregressive models, namely LSTAR and ESTAR models. The essential part of the work is devoted to the derivation of tests for linearity against the alternative of the re- levant nonlinear model. There is also shown how to estimate the parameters of these models along with the selection procedure between the LSTAR and the ESTAR model. A simulation study was carried out, which deals with the power of linearity tests. At the end of the thesis, we applied the theory to some real data and we estimated the appropriate model for their representation. 1
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Seasonal exponential smoothing
Rábek, Július ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This thesis deals with the issues of time series modeling, where seasonal component is present. Principles of basic seasonal exponential smoothing methods: simple and double exponential smoothing, Holt's method, which are applicable on time series without seasonality, are described in the beginning. For seasonal time series, Holt-Winters exponential smoothing is the most suitable method. This method is introduced in both of its versions and the usage of either version depends on the characteristics of the seasonal component. Furthermore, state space modeling is presented as a statistical framework for exponential smoothing methods, joined with a discussion of some selected problems related with practical implementation of these techniques together with suggestions of their solution. Finally, Holt-Winters method on two real data time series with seasonality is presented.
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Special aspects of non-linear time series modelling
Studnička, Václav ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
Various models, such as ARMA and GARCH, are used in the financial time series framework. The purpose of this thesis is to present an alternative for these models which are bilinear time series models. First chapter is theore- tical, there is a short introduction to the theory of time series and ARMA models. Second chapter focuses on theoretical aspects of the simple bilinear model, third chapter presents the theory for general bilinear model in the similiar fashion as for simple model. Last chapter is focused on practical aspects, it contains simulations and examines the properties of estimates based on the presented theory, final part is devoted to the comparison of properties of ARMA models and bilinear models for selected financial data. 1
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Smooth Transition Autoregressive Models
Khýr, Miroslav ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The aim of this work is describing theory of smooth transition autoregressive models, namely LSTAR and ESTAR models. The essential part of the work is devoted to the derivation of tests for linearity against the alternative of the re- levant nonlinear model. There is also shown how to estimate the parameters of these models along with the selection procedure between the LSTAR and the ESTAR model. A simulation study was carried out, which deals with the power of linearity tests. At the end of the thesis, we applied the theory to some real data and we estimated the appropriate model for their representation. 1
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