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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.
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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.
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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.
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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.
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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
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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.
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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.
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Methods of dynamical analysis of portfolio composition
Meňhartová, Ivana ; Hanzák, Tomáš (advisor) ; Cipra, Tomáš (referee)
Title: Methods of dynamical analysis of portfolio composition Author: Ivana Meňhartová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomáš Hanzák, KPMS, MFF UK Abstract: In the presented thesis we study methods used for dynamic analysis of portfolio based on it's revenues. The thesis focuses on Kalman filter and local- ly weighted regression as two basic methods for dynamic analysis. It describes in detail theory for these methods as well as their utilization and it discusses their proper settings. Practical applications of both methods on artificial data and real data from Prague stock-exchange are presented. Using artificial data we demonstrate practical importance of Kalman filter's assumptions. Afterwards we introduce term multicolinearity as a possible complication to real data applicati- ons. At the end of the thesis we compare results and usage of both methods and we introduce possibility of enhancing Kalman filter by projection of estimations or by CUSUM tests (change detection tests). Keywords: Kalman filter, locally weighted regression, multicollinearity, CUSUM test
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Seasonality and periodicity in time series
Musil, Karel ; Jonáš, Petr (advisor) ; Cipra, Tomáš (referee)
This work deals with periodicity and seasonality in time series. After a time series periodicity topic is introduced, a seasonal component of time series and a seasonal adjustment is presented. Then basic approaches, used in current practice, are introduced. These are classic model approach, Box-Jenkins methodology, and spectral analysis. The described seasonal adjustment techniques are applied to the time series of the Czech import, export, and foreign trade balance. A brief description of potential problems, which are connected to the seasonal adjustment and are common in practice, is a part of the example as well.
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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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