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Classification Ratemaking
Valášková, Zuzana ; Mandl, Petr (referee) ; Mazurová, Lucie (advisor)
In the present work we will study methods, which are used to find a premium in nonlife insurance according to the grouping risks into the risk groups. These risk groups are constructed according to the concrete indices. All work consists of the three main sections. At the end you can find example, where all methods are applied. First section explains the basic methods which can be used in ratemaking: the weighted least square method, the method of marginal totals and the method of Bailey - Simon. The second section studies more sophisticated method for ratemaking: The generalized linear models. The third section studies the credibility estimations used in ratemaking, which are important and used today.
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The projection of population mortality tables
Balajová, Helena ; Mazurová, Lucie (referee) ; Kořistka, Jan (advisor)
In the present work we deal with the problem of projecting mortality. At the beginning we describe the life table and we classify the methods and models (parametric models, non-parametric models, models based on reduction factors). The Lee - Carter method is described in detail. We focus on forecasts for a group of countries. We show existence of common trend in mortality in Europe and its disappearance. We assume that demograpahical characteristics of di erent countries with similar socioeconomic conditions will converge in the future. We apply this assumption using the augmented Lee - Carter model, in which selected countries have same trend in mortality as a group with lower mortality, and using Broekhoven approach, which determines that the mortality in given year in the future will be the same as in chosen group. In the last chapter we apply these methods in Central Europe.
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Insurance and risk measures
Vašek, Lukáš ; Justová, Iva (referee) ; Mazurová, Lucie (advisor)
In the present work we attend to methods proposed in actuarial literature to quantification and evaluation of risk. We show various approaches in construction measures of risk and we analyze properties they satisfy. We introduce theory of equivalent utility and dual theory of risk and than we concentrate our mention especially on the distorted measures of risk. Due to quantity of riskiness we study rate of risk loading and the height of distortion parameters.
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Yield Decomposition in Life Insurance
Molnár, Vladimír ; Mazurová, Lucie (referee) ; Král, Filip (advisor)
The diploma thesis tackles a topic, that falls into much wider range of problems called nancial modeling. The aim of the thesis is to show how to analyze technical pro t in life insurance and identify sources of the pro t. For that, cash ow model is constructed. During the construction some key aspects of how to choose actuarial assupmtions are brie y discussed. Model is applied to a traditional life insurance product.
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Annuities under random interest rates
Sviteková, Zuzana ; Mazurová, Lucie (referee) ; Cipra, Tomáš (advisor)
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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Multidimensional Bonus Malus Systems in Non-life Insurance
Drábková, Miroslava ; Mazurová, Lucie (referee) ; Mandl, Petr (advisor)
Bonus-malus systems are tariff systems which determine premium depending on clairn history of insured risks in previous periods. The thesis deals with computation of part of risk which falls on policy holders and on insurance company. There is used the Bayesian approach in the first part. A portfolio is assumed in which the risk parameter of each policy holder is a random variable. There is established a model with two kinds of policy holders too, every kind has a given distribution of the risk parameter again. There are mentioned some bonus-malus systems used in the world in third-party liability insurance in the second part. It is shown how to modify the systems which do not satisfy the Markovian condition to a model which satisfies this condition. It is useful for next calculations. A portfolio is assumed again in which the risk parameter of each policy holder is a random variable and it is computed part of risk which falls on policy holders and on insurance company. The calculations are supplemented by concrete numerical iII ustrations.
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Multivariate GARCH
Maďar, Milan ; Hurt, Jan (advisor) ; Branda, Martin (referee) ; Mazurová, Lucie (referee)
4 Title: Multivariate GARCH Author: Mgr. Milan Mad'ar Department: Katedra pravděpodobnosti a matematické statistiky Abstract: This thesis will examine the regional and global linkages as evi- dence of integration of stock markets in Frankfurt, Amsterdam, Prague and the U.S. Therefore we will utilize the multivariate GARCH approach that investigates the dynamics of volatility transmission of related foreign exchange rates. Also, we will define three basic model classes. For each of the model classes a theoret- ical review, basic properties and estimation procedure with proofs are provided. We illustrate each approach by applying the models to daily market data. The two main aims of the thesis are to discuss and report the existence of regional and global stock markets linkages and provide a comparison of such multivariate GARCH models on the data sample. The main contribution of the thesis is that it treats the data in the context of real development in financial markets and takes into account the real situation during and after the financial crisis of 2008. We find out that the estimated time-varying conditional correlations indicate limited integration among the markets, which implies that investors can benefit from the risk reduction by investing in the different stock markets, especially during the crisis....
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Traditional and modern approaches to pricing in nonlife insurance
Vojtěch, Jonáš ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
Title: Traditional and modern approaches to pricing in nonlife insurance Abstract: This thesis deals with the theory and implementation of generalized linear models in the area of pricing of non-life insurance and subsequent optimalization of rates. Using the generalized linear models it is possible to estimate expected value and variance of compound distribution of total claims made according to insurance policy during definite time period. The next step is to build an optimalization model and describe several methods how to determine rates that lead to optimal distribution of safety margins within insurance policies in particular risk groups. Represented approaches how to calculate insurance premiums are numerically illustrated on simulated data in concluding parts of the thesis.
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