|
|
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
|
|
|
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.
|
|
|
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
|
|
|
Parametrizace rozdělení škod v neživotním pojištení
Špaková, Mária ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
Title: Parameterization of claims distribution in non-life insurance Author: Bc. Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta Ph.D., MFF UK Abstract: This paper deals with the parameterization of claim size distributions in non-life insurance. It consists of the theoretical and the practical part. In the first part we discuss the usual distributions of claims and their properties. One section is devoted to extreme values distributions. Consequently, we mention the most known methods for parameter estimation - the maximum likelihood method, the method of moments and the method of weighted moments. The last theoretical chapter is focused on some validation techniques and goodness-of-fit tests. In the practical part we apply some of the discussed approaches on real data. However, we concentrate mainly on the large claims modeling - firstly, we select a reasonable threshold for our data and then we fit the claims by the generalized Pareto distribution together with the introduced parameterization procedures. Based on the results of the applied validation methods we will choose appropriate models for the biggest claims. Keywords: parameterization, non-life insurance, claims distribution.
|
|
|
Stochastic Loss Reserving Models
Košová, Nataša ; Justová, Iva (advisor) ; Cipra, Tomáš (referee)
In present thesis we study and describe a stochastic loss reserve model for individual insurers. Specifically, it is the model based on the three following features. Modelling of expected claims depends on unknown parameters which estimates need to be the most accurate. Aggregated occurred and paid losses for particular years are modelled by a collective risk model. The final reserve is estimated by Bayesian methodology that uses a prior information from a significant number of insurers. Part of the thesis is also an implementation of the program that calculates reserves by using our model and its testing on simulated data.
|
|
|
Multivariate Financial Time Series
Veselý, Daniel ; Cipra, Tomáš (advisor) ; Kopa, Miloš (referee)
In this work we will describe methods for modeling multivariate financial time series. We will concentrate on both modeling expected value by multi- variate Box-Jenkins processes and primarily on modeling conditional corre- lations and volatility. Our main object will be DCC (Dynamic Conditional Correlation) model, estimation of its parameters and some other general- izations. Then we will programme DCC model in statistical software R and apply on real data. In applications we will concentrate on problem of high dimension of financial time series and on modeling conditional correlations data with outliers.
|
|
|
Longevity Risk in Life Insurance
Danešová, Zdenka ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
In this thesis we deal with the longevity risk originating from the uncertain future evolution of mortality at adult-old ages. It may emerge in particular because of an unanticipated reduction in mortality rates. That risk is significant for annuity and pension providers. We consider a model portfolio represented by one cohort of recipients of immediate life annuities. We introduce possibilities for assessing the risk of such portfolio. A comparison of the impact of longevity risk is made with random deviations in mortality rates. We also deal with the question of solvency of the insurer by investigating the solvency capital requirement for longevity risk.
|
|
|
Nonlinear nonparametric models for financial time series
Klačanská, Júlia ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The thesis studies nonlinear nonparametric models used in time series analy- sis. It gives basic introduction to the time series and states different nonlinear nonparametric models including their estimates. Special attention is paid to three of them, CHARN, FAR and AFAR model. Their properties and esti- mation techniques are presented. We also show techniques that select values of the parametres used further in estimation methods. The properties of time series models are investigated in simulation and real data studies. 1
|
|
|
Software products for financial time series analysis
Vlasáková, Romana ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The present work deals with selected methods suitable to work with financial time series. Firstly, univariate linear models ARMA are introduced, followed by the description of volatility models ARCH and their generalization to GARCH models. There are many modifications of standard GARCH models designed with respect to the nature of financial data, some of which are presented. Another part of the work dealing with multiple time series focuses on VAR models and bivariate GARCH models. The most important part of the work are practical examples of building the theoretically described models in various types of software with built-in procedures for time series analysis. We apply five different types of commercial and non-commercial software, namely EViews, Mathematica, R, S-PLUS and XploRe. The used software products are presented and compared in terms of their capabilities and the results obtained for particular methods.
|
|
|
Annuity modelling in MTPL
Eštóková, Agáta ; Kočová, Karolína (advisor) ; Cipra, Tomáš (referee)
Title: Annuity modelling in MTPL Author: Bc. Agáta Eštóková Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Karolína Kočová Supervisor's e-mail address: kkocova@koop.cz Abstract: This diploma thesis focuses on the possibilities of using generational mortality tables for third party liability insurance, mainly for bodily injured. It describes the construction of generational mortality tables and the creation of RBNS claims reserves. Besides the demonstration of these models, the work analyzes the results of calculating reserves in accordance with generational mortality tables and actual mortality tables of the Czech Republic. An impor- tant element in provision calculating is the simulation of future life expectancy of the insured, i.e. random generation of life expectancy based on generational mortality data. Characteristics of the distribution of reserves are derived from simulations. Furthermore, we compare the results of stochastic and determi- nistic approach of computing the reserves. Keywords: third party liability insurance, RBNS, annuity, generational morta- lity tables.
|
guest ::
