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Optimal pricing in nonlife insurace
Ďurošková, Zuzana ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
V této práci se zabýváme základními principy tvorby sazeb neži- votního pojištění. Pracujeme s rizikově heterogenním portfóliem obsahující ur- čitý počet rizikových tříd. Cílem je najíst optimální sazbu pojistného pro kaž- dou třídu. K nalezení aplikujeme optimalizační modely a využíváme nelineárního programování. Formulujeme a řešíme optimalizační problém za jistých podmínek. Odvodíme jeho optimální řešení, z kterého vyjádříme a popíšeme r·zné principy pro výpočet pojistného pro každou třídu. Zavedeme taktéž duální optimalizační problém a ukážeme tvar jeho optimálního řešení. V numerické studii vypočítáme z odvozených metod sazby pojistného, kde pro jednotlivá rizika reprezentující úhrny škod, budeme volit konkrétní rozdělení. 1
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Excess of loss reinsurance with reinstatements
Čápová, Petra ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
This thesis deals with the calculation of the premium for model of excess of loss reinsurance with reinstatements (XL-reinsurance with reinstatements). In the first part except the description of the basic model, we devote to derivation of the formula for calculating the pure premium. Furthermore, we show the detailed calculation procedure of the pure premium including the derivation of the probability function for the composite distribution of the total reinsurer's participation in claims here. The thesis also describes the method of PH transformation, which is used to determine the risk adjusted premium. In the second part we show these procedures on concrete examples for various probability distributions of the amount of claims and the number of claims. Powered by TCPDF (www.tcpdf.org)
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Dependence analysis of categorical data from banking
Khýr, Miroslav ; Zichová, Jitka (advisor) ; Mazurová, Lucie (referee)
Title: Dependence analysis of categorical data from banking Author: Miroslav Khýr Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathema- tical Statistics Abstract: The aim of this work is describing in detail the theory of the log - linear expansion and graphical models for random vectors with a discrete distribution. Such vector can be used for modeling categorical variables for example in a po- pulation of borrowers by a bank . We show how to estimate the probability of an individual category. We use a log - likelihood function. Independence graph can represent conditional independence of discretely distributed random variables. Using this theory, especially using deviance as test statistics, we can examine whether same data correspond to the selected graphical model. At the end of this work we apply the described theory to real data and determine the graphical mo- del best fitting the dependence structure in a database from banking. From this graph we can deduce which variables are dependent and which are independent. Keywords: Log - linear expansion, graphical model, log - likelihood function ,de- viance.
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Risk measures in finance and insurance
Krch, Ivan ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee)
The main aim of this thesis is to examine risk measures which are used in finance and insurance. This work is focused on describing their mathematical characterizations and their relationships. In this thesis are discussed coherent risk measures, spectral risk mea- sures and distorted risk measures. Considerable attention is given to value at risk which is connected to a certain extent with all risk measures which are mentioned above. Attention is also aimed on using of these risk measures on illustrative examples which make their characteristic clear. Further there are demonstrated risk measures for quantification risk of portfolio based on real data. 1
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Multidimensional Credibility
Zhuravova, Nadezda ; Mazurová, Lucie (advisor) ; Pešta, Michal (referee)
The aim of this graduation work is theoretically describe and also demonstrate the practical application of the theory of credibility in the multidimensional case. This theory is one of the most frequently used methods for calculating premiums, expected claims frequency or the expected average amount of damage. In this work we describe multidimensional Bühlmann-Straub credibility model and two- dimensional model with a known distribution. For each of these models we derive credibility estimate and examples of using these estimates in practice. Both models are compared on simulated data. 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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Generalized Linear Models in Insurance
Staněk, Petr ; Mazurová, Lucie (advisor) ; Pešta, Michal (referee)
In the present thesis we study Generalized linear mo- dels with their application in the insurance. Our specifiation is in using Poisson and Binomial distribution. Our goal is application of the theoretical knowledge in the vehicle insurace, claim reserving and survival model. Keywords: Link, linear predictor, response variable, explanatory variable, likelihood function, quasilikelihood function, deviance, re- ziduals, survival model, run-off triangle, canonical link, Poisson dis- tribution, binomial distribution, dispersion parameter, variance func- tion. 1
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Stochastic modelling of mortality development
Škerlík, Peter ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
In the presented diploma thesis we study possibilities of forecasting mortality rates and we explain the most used models to measure it. The longevity and mortality risk are characterized and options for transfer of risks to other subjects are suggested. Further we applied LifeMetrics tool to predict mortality and quantify longevity risk in our data set, also possibilities of its usage are described in more details. The aim of the work is to provide the reader with sufficient amount of theoretical information about the used stochastic models for mortality prediction. Also the work may be helpful to gain deeper knowledge about longevity risk.
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Operational risk modelling
Mináriková, Eva ; Mazurová, Lucie (advisor) ; Hlubinka, Daniel (referee)
In the present thesis we will firstly familiarize ourselves with the term of operational risk, it's definition presented in the directives Basel II and Solvency II, and afterwards with the methods of calculation Capital Requirements for Operational Risk, set by these directives. In the second part of the thesis we will concentrate on the methods of modelling operational loss data. We will introduce the Extreme Value Theory which describes possible approaches to modelling data with significant values that occur infrequently; the typical characteristic of operational risk data. We will mainly focus on the model for threshold exceedances which utilizes Generalized Pareto Distribution to model the distribution of those excesses. The teoretical knowledge of this theory and the appropriate modelling will be applied on simulated loss data. Finally we will test the ability of presented methods to model loss data distributions.
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Double chain ladder
Perichtová, Margaréta ; Pešta, Michal (advisor) ; Mazurová, Lucie (referee)
This thesis deals with one of the biggest problems in non-life insurance and that is forecasting outstanding claims liabilities. Chain ladder method is probably the most often used method for estimating outstanding liabilities. Firstly, we show classic chain ladder method and its deterministic and stochastic form. Secondly, we introduce relatively new method, double chain ladder method which comes from chain ladder method, but in addition it considers number of reported claims, that allow us to count RBNS reserve more precisely and also to count IBNR and RBNS reserves separately. In the end we apply both methods on the real data. We compute point estimate of the reserve by chain ladder method and by double chain ladder method and compare the results. Powered by TCPDF (www.tcpdf.org)
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