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Econometric systems of simultaneous equations in life insurance
Hendrych, Radek ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
In present work we deal with theoretical and practical issues related to econometric systems of (linear) simultaneous equations. In the first chapter we introduce to theoretical aspects of this problem. We devote considerable space to estimation procedures and comparisons of their properties, mention questions of identification, an inconsistency of OLS-estimates for the simultaneous modeling, tests of hypotheses specific to this area, dynamic systems and constructions of forecasts in models. In the second chapter we introduce selected basic concepts relevant to life insurance. In the third chapter we show the practical application of theoretical knowledge in the event of an econometric model of financial flows in the life insurance company operating on the Czech market. We compare ordinary estimation procedures (2SLS and 3SLS approach), perform some tests, which serve us to verify selected information on the studied model. We show the possibility of using residual bootstrap, including examples of use in the construction of confidence intervals. Finally we analyze several predictions of the estimated model of the life insurance company for predetermined scenarios for the development of selected variables, which is very important from practical point of view.
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Statistical Properties of the Estimate of Non-Life Insurance Technical Reserves
Pechanec, Jan ; Jedlička, Petr (advisor) ; Cipra, Tomáš (referee)
In the presented work we study two different statistical methods for estimating IBNR reserve that is a part of the reserve for outstanding claims reserves. The first method is stochastic version of the Chain ladder method and the second one is a PTF model. We describe theories of the methods and show their different properties. The Chain ladder method does not assume any distribution of claims amount, on the other hand PTF models assume normal distribution of logarithms of incremental data. In practical part of this work we apply both methods on illustrative data and then we compare the results. We inspect especially probabilistic distribution of estimate of reserves and their statistical characteristics. An important part of this work is statistical testing of assumptions of both methods.
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Selected topics of multivariate time series analysis in finance
Slívová, Iveta ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
In the present work, we study ARMA model at the beginning, then we write about one-dimensional and multivariate ARCH and GARCH model, further we move on to the multivariate GARCH model. At the end, the principal component decomposition is introduced, it is a procedure to reduce the number of parameters involved in a multivariate GARCH model. The theory is explicated rst on a basic ARMA model, afterwards it is modi ed step by step for the one-dimensional and the multivariate GARCH model. There are solved examples for multivariate ARCH and GARCH model and nancial data are analyzed by means of these models.
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Modelling financial time series
Holubářová, Šárka ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
This diploma thesis deals with modelling nancial time series and especially the changing volatility of nancial returns, which is characteristic for them. The theoretical part of the thesis describes several processes with non-constant conditional variance, which form an alternative to the classical ARMA approach to modelling time series. The focus is mainly on two types of processes - lognormal autoregressive process for conditional variance as an example of process where the conditional variance is independent of past returns, and on ARCH processes which to the contrary are based on dependence of the conditional variance on past returns. The properties of described models are veri ed and demonstrated in a simulation study carried out in Mathematica. Final part of the thesis is dedicated to application of the models to real data and modelling volatility of time series of returns of shares and currency rates. The parameters of the models are estimated and forecasts calculated in Mathematica with partial use of programme XploRe.
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Variable life annuity
Šimlovič, Matej ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
In the first chapter, the thesis contains a description of variable annuity and description of four basic guarantees: guaranteed minimum death benefit, guaranteed minimum accumulation benefit, guaranteed minimum income bene- fit and guaranteed minimum withdrawal benefit. For each of these guarantees, there is a description of principle of the benefit, assumptions of payment, amount of payment and a difference from a product without such guarantee, thus a net benefit from the guarantee. In the second chapter, with additional assumptions, there are deductions of expected values of benefits from the described guaran- tees and numerical calculation of these expected values for both genders, various entering ages and various investment variables. 1
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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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Retirement planning
Langová, Nadežda ; Cipra, Tomáš (advisor) ; Hurt, Jan (referee)
The thesis is concerned with optimal retirement pension planning in the framework of the Czech pension system. The work proposes an unavoidable reform in order to compensate for adverse demographic trends. Subsequently, it introduces mathematical methods for future old-age pension determination in private pensions. Equally, the thesis deals with optimal pension strategies: when the benefits of individual old-age insurance outgrow those of institutionalised pension insurance and vice versa. A particular aspect of the reform where participants can partially opt out from the compulsory pillar and become part of the new system is discussed with emphasis on the opt-out accompanying factors.
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Annuities under random interest rates
Sviteková, Zuzana ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee)
The thesis describes accumulated values of annuities with yearly payments under independent random interest rates. The thesis focuses on general annuities with payments varying in arithmetic and geometric progressions which are important varying annuities. Mean and variance formulae of the final values of the annuities are derived in the thesis. In the beginning (chapter 2) the formulae of the final values of the annuities under xed rates of interest are shown. Chapter 3 is the main part of the thesis. The mean and variance formulae of the final values of the annuities under random rates of interest are proofed here. The thesis is based on the article [4] and [1]. It is especially focused on the article [1] which corrects main outcome of the article [4]. In the end (chapter 4) special cases of the annuites with numerical and graphical solutions are shown.
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