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Computing the aggregate claims distribution
Dlouhá, Veronika ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
In this bachelor thesis I study the distribution of aggregate claims. First I introduce the topic and present main models. Then, I show some distributions used for modeling number and amound of claims with estimates of their parameters. Next I get to compound distribution and its basic charakteristics. In other parts of the thesis I study the probability of aggregate claims using Panjer recursion and fast Fourier transform and apply the thoery to examples. Finally I mention some methods to approximate aggregate claims using known distribution.
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Some modifications of models ARCH for financial time series
Nekvinda, Matěj ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This work deals with modelling time series, especially their volatility, by methods based on the ARCH model. In the beginning, we describe the general features of financial time series, afterwards we focus on the ARCH model modifications. The described modifications are GARCH, EGARCH, GJR-GARCH and briefly GARCH-M, IGARCH, FIGARCH and QGARCH. Along with the models, there is a description of their behaviour, which frequently reflects some features of financial time series. We also mention the process of practical financial time series analysis. In the end, we demonstrate the application of GARCH, EGARCH and GJR-GARCH models for modelling values of FTSE 100 index together with diagnostic tests and prediction. Powered by TCPDF (www.tcpdf.org)
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Some quantitative aspects of life annuities
Šťástka, Petr ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee)
The aim of this diploma thesis is describe the most common methods of financing pension plans, focusing on some of the methods of fund financing pension plans. To describe the individual methods, their numerical illustration and allow comparison, it is necessary to dispose of necessary instruments. Therefore in the thesis there are constructed the cohort life tables for the Czech Republic. The thesis also deals with the modelling life annuities in continuous time, in particular, with the shape of im- mediate pension anuity factor for Gompertz law of mortality. Namely, this factor is one of the parameters entering the calculation of the individual methods of fund fi- nancing for pension plans.
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Penzijní modely
Kalaš, Martin ; Cipra, Tomáš (advisor) ; Branda, Martin (referee)
The thesis is concerned with the problem of sustainable spending towards the end of the human life cycle, which is a substantial quantitative problem in the pension framework. We gradually build a model, which coherently links the three key factors of retirement planning: uncertain length of human life, uncertain investment returns and spending rates. Within the framework of our intuitive model, we apply the method of moment matching to derive an approximation for the probability of individual's retirement ruin. The accuracy of presented approximation is analyzed via extensive Monte Carlo simulations. A numerical case study using Czech data is provided, including calculated values for the probability of ruin and maximal sustainable spending rate under various combinations of wealth-to-spending ratios and investment portfolio characteristics.
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Mortality projections by cause
Štádlerová, Kateřina ; Kořistka, Jan (advisor) ; Cipra, Tomáš (referee)
The thesis focuses on the mortality projections by causes of death. The thesis includes also the application of such knowledge on the data of the Czech population. The mortality projections are used nowadays more and more often due to the population ageing. The results of this thesis may be interesting both for financial institutions such as insurance companies and for the purposes of certain areas of government policy with regards to the pension planning. So far not many articles have been published in the Czech language, nor are there any published results of similar projections using the data derived from the Czech environment. Powered by TCPDF (www.tcpdf.org)
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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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Financing post-retirement income
Skřivanová, Zuzana ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
This thesis deals with various possibilities of the financing post-retirement income. In the first part, the basic knowledge from the area of demography is given, what is necessary for the determination of mortality assumptions and for the computation of cash flows in post-retirement age. Subsequently models of decumulation periods are theoretically compared - the basic variants are purchasing of life annuity and annuity-certain, from which are derived selected combinations and modifications. In the last part, theoretical bases are used to determining specific mortality assumptions with respect to the computed values of parameters of the Gompertz-Makeham mortality law. Subsequently cash flows of particular models are numerically illustrated with respect to the mortality assumptions.
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Modely celočíselných časových řad s náhodnými koeficienty
Burdejová, Petra ; Prášková, Zuzana (advisor) ; Cipra, Tomáš (referee)
Title: Models of integer-valued time series with random coefficients Author: Petra Burdejová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Zuzana Prášková, CSc. Abstract: In the presented thesis, a generalized integer-valued autoregres- sive process of the order p (GINAR(p)) is considered first. The main aim is taken to introduction of random coefficient integer-valued autoregressive process (RCINAR(p)). We use a thinning operator in order to define the processes. The main characteristics of GINAR(p) and RCINAR(p) are obtained. Condi- tions for stationarity and ergodicity are stated. Three methods of estimation (Yule-Walker, Conditional least squares, Generalized method of moments) are given and compared in simulation with respect to the mean squared error (MSE). At the end, RCINAR(3) model is applied to a real dataset representing a number of earthquakes per year. Keywords: thinning operator, random coefficients, integer-valued time se- ries, GINAR, RCINAR
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Methods for mortality forecasting and longevity risk
Počerová, Veronika ; Branda, Martin (advisor) ; Cipra, Tomáš (referee)
The main aim of this thesis is to analyse different mortality models regarding the longevity risk. We focus on the well-known stochastic models (Lee-Carter model, Age-period-cohort model by Renshaw and Haberman, Cairns-Blake-Dowd two-factor model) and compare them with relatively new Taiwanese model by Yang, Yue and Huang which is based on principal component analysis. Both the theoretical and also the empirical parts are included. Empirical part evaluates all the models mentioned above on the Czech mortality data from 1970-2000 for individuals aged between 50-100 years. Final mortality predictions are made for next 30 years.
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Some possibilities of heteroskedasticity modeling with applications to non-life insurance
Pavlačková, Petra ; Zimmermann, Pavel (advisor) ; Cipra, Tomáš (referee)
Title: Some possibilities of heteroskedasticity modeling with applications to non-life insurance Author:Petra Pavlačková Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Zimmermann Pavel, Ph.d. Abstract: This thesis deals with the possibilities of modeling heteroskedasticity using generalized linear models. It summarizes the assumption for these models and their application in practice. It shows the practical need for these models. Furthermore, the thesis deals with the modeling of variance using other methods than generalized lienar models - such as generalized additive models or local regression. Comparison of methods is graphically demonstrated. Keywords: Dispersion parameter, variance function, Joint modelling of mean and dispersion
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