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Solvency II: solvency in insurance
Čáha, Pavel ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee)
This thesis is dedicated to Solvency II, a regulatory framework for insurance and reinsurance companies effective in European Union. Firstly, it explains the notion solvency and also describes the principles of the regulation itself. Another part is focused on the calculation of solvency capital requirement and minimal capital requirement, using standard formula. The capital requirements are derived on the level of risk modules and their submodules. Furthermore, the topic of technical reserves is discussed and emphasis is placed on the derivation of mean square error of prediction. Described methods are Chain-Ladder and Bornhuetter-Ferguson. The last part of the thesis includes the calculation of capital requirements for real data. A program SolvencyII.xlsx that shows particular derivations is enclosed.
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Value-at-Risk Calculation Using Extreme Value Theory
Lipták, Patrik ; Hendrych, Radek (advisor) ; Mazurová, Lucie (referee)
This diploma thesis studies extreme value theory and its application in finan- cial risk management, when focusing on computation of well-known risk measure - Value at Risk (VaR). The first part of the thesis reviews theoretical background. In particular, it rigorously discusses the extreme value theory when emphasi- zing fundamentals theorems and their consequences followed by the summary of methods based on this theory, specifically, Block Maxima method, Hill met- hod and Peaks over Threshold method. Moreover, specific issues that may arise in such applications and ways how to deal with these problems are described. The second part of the thesis contains extensive empirical study, which together with theoretical foundings applies each of the examined method to real market data of the closing prices of Dow Jones Industrial Average stock index, stocks of JPMorgan and stock index Russell 2000 in order to compare methods based on extreme value theory together with the classic methodology RiskMetrics. 1
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Parametric risk modelling in assessing mortality
Hlavandová, Radana ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
In this thesis we focus on modeling stochastic mortality and parameter risk in assessing mortality. We explore two mortality stochastic models for modeling the number of deaths in portfolio which consist of one or more than one cohort. We define the term mixture of distributions and introduce Beta-Binomial and Poisson-Gamma model. We address immediate life annuities and we apply Bayesian Poisson- Gamma model to quantify longevity risk on data. The obvious increasing trend of average lifetime leads insurance companies to greater protection against longevity risk. We show how to deal with solvency rules by internal models designed consistently with the requirement in the standard formula of Solvency II. Powered by TCPDF (www.tcpdf.org)
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LDA approach to operational risk modelling
Kaplanová, Martina ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
In this thesis we will deal with the term of operational risk, as it is presented in the directives Basel 2 that are mandatory for financial institutions in the European Union. The main problem is operational risk modeling, therefore, how to measure and manage it. In the first part we will look at the possibility of calculating the capital requirements for operational risk under Basel 2, mainly the calculation with the internal model. We will describe the specific procedures for the development of the internal model and we will focus on Loss Distribution Approach. The internal model will be based on modeling of loss in each risk cell separately. In the second part we will show, how to include modeling of dependence structure between risk cells to the internal model with using copulas. Finally, we will show the illustrative example, where we will see, whether the modeling of dependence leads to a reduction of the total capital requirement. Powered by TCPDF (www.tcpdf.org)
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Stochastic mortality modeling for multiple populations
Skřivanová, Zuzana ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
Title: Stochastic mortality modelling for multiple populations Abstract: This thesis deals with the possibilities of modelling and forecasting of age-specific mortality rates. The introductory part summarizes the basic terms from demo- graphy, which are related to mortality, and specifies elementary approaches to the mortality modelling. Subsequently there are in detail described the three most commonly used stochastic mortality models - Lee-Carter, Renshaw-Haberman and Cairns-Blake-Dowd. The fundamental part of this thesis deals with the possi- bilities of using these models for mortality modelling simultaneously in correlated populations. These theoretical bases are in the final part of this thesis numerically illustrated on the mortality models for populations of Czech and Slovak Republic. 1
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Capital allocation principles
Dvořák, Daniel ; Mazurová, Lucie (advisor) ; Hurt, Jan (referee)
Insurance companies or other financial institutions face financial risks during their various activites. Risk capital is allocated in order to cover these risks. The goal of capital allocation is to redistribute this capital to various constituents of the firm with respect to their riskiness. The thesis deals with risk measures and allocation methods. Special emphasis is put on the notions of coherent risk measures and coherent allocation methods. Conditions of coherence are checked for certain allocation methods. The thesis also deals with practical calculation of allocations to individual risks using allocation methods. 1
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Proportional reinsurance
Kubišová, Barbora ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
This thesis deals with the issue of proportional reinsurance. It describes the basic types of proportional reinsurance, Quota Share, Surplus and their modi- fications, Variable Quota Share and Table of Lines Surplus. Furthermore, the paper explains how reinsurance changes aggregate claim amounts in the indivi- dual risk model. In this thesis we introduce two criteria for finding optimal ratio of proportional reinsurance. First, the de Finetti's criterion which minimizes the variance of the result of the insurer subject to a given level for the expected re- sult. Second is the optimality criterion which minimizes the (conditional) value at risk of total costs of the insurance company. Finally, we present numerical examples where on the basis of optimality criteria we find the optimal quota, respectively optimal retention level of the reinsurance. 1
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Claims reserving with copulae for multiple lines of business
Valentovičová, Katarína ; Pešta, Michal (advisor) ; Mazurová, Lucie (referee)
Claims reserving and claims process estimation present classical problems in general insurance. The overall reserves are often determined under the assumption of independence among the lines of business. Though, recently modelling of the dependence among multiple lines of business has become crucial issue of reserving process. In this context, copulae provide a useful tool to construct models which go beyond the classical ones in terms of dependence structure. This thesis deals, in particular, with the copula regression model, its properties and possible applications in general insurance. This approach combines GLM modelling of margins and then expressing the dependence structure using copula. The theoretical methods are illustrated on a real dataset.
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Insurance pricing methods based on risk measures
Malá, Kateřina ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
In this thesis we study various risk measures and one of their characteristics - the coherence. We talk especially about value-at-risk (VaR in short), respectively about conditional value-at- risk (CVaR). We also mention the advantage of CVaR against VaR. After that we discuss the most common forms of compound distribution that are used in practice. The final part of this bachelor thesis is dedicated to a numerical study where we calculate mean, variance, VaR a CVaR for specific values of parameters.
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Granular loss models in reserving
Bílková, Kristýna ; Pešta, Michal (advisor) ; Mazurová, Lucie (referee)
Claims reserving methods usually use data aggregated into development triangles, therefore a lot of information that insurance companies possess remains unused. This thesis shows a triangle-free approach using granular information from a claim by claim database. A statistical model for claims development which can further be used for estimation of reserves is built. The statistical model consists of a counting process that drives claims occurrence, distribution of reporting delay and distribution of claims severity. Several suitable distributions are presented, as well as methods for obtaining their parameters from data. Theoretical apparatus is used for real data. The thesis also pursues comparison of the IBNR reserve estimation using the triangle free approach and distribution free Chain ladder method for real data as well as for simulated data sets. For the data used in this thesis the complexity and data requirements of the triangle free approach are in favor of more preciseness and versatility. Powered by TCPDF (www.tcpdf.org)
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