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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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Recursive calculation of compound distributions
Sekera, Michal ; Mazurová, Lucie (advisor) ; Pešta, Michal (referee)
The aim of this work is the calculation of compound distributions by using the algorithm known as the Panjer recursion. This algorithm is limited to dis- crete distributions and the (a, b, 0) and (a, b, 1) classes of distributions. The thesis shows which distributions are members of these classes. The thesis then descri- bes the discretization of continuous distributions by using the rounding method and the method of local moments matching; everything is explained on exam- ples. These methods are then applied to the calculation of the premium for mo- del of excess of loss reinsurance with reinstatements (XL-reinsurance with re- instatements), and the calculating the solvency capital requirement. Numerical illustrations are included. 1
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Credibility models for claim frequency
Biolek, Jiří ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
The work deals with estimation of unknown risk parameters of a driver. Risk parameter indicates how many times more accidents we may expect from this driver compared with the average insurance group to which the driver is assigned according to the precarious classification. Risk parameter is a random variable, which is depending on the damage share of this driver. The second and third chapters describe the derivation of the estimates that minimize the quadratic and exponential loss function. It also compares the level of these estimates and the convergence rate. In chapter four there are several simulations performed and tables with estimates for any specific data created. 1
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Pricing in non-life insurance
Ondrušková, Markéta ; Mertl, Jakub (advisor) ; Mazurová, Lucie (referee)
The aim of this thesis is to determine the premium of motor third party liability insurance. Thesis explores both direct approach to premium cal- culation and calculation using separately calculated claims frequency and claims severity. Emphasis is put on the use of generalized linear models whose theory is also present. Described approaches to calculation are applied on real world data, compared with each other and then final model for premium calculation is selec- ted. Premium is determined with the inclusion of IBNR reserves and expenses. Keywords: generalized linear model, claims frequency, claims severity, net pre- mium, gross premium, motor third party liability insurance, bonus-malus. 1
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Multivariate GARCH
Maďar, Milan ; 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 the integrated markets consist of stock markets in Frankfurt, Amsterdam, Prague the U.S. Therefore we will utilize the multivariate GARCH approach that investigates into 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 theoretical review, basic properties and estimation procedure with proofs are provided. We illustrate approach by applying the models to daily market data. Our two main aims are discussing and reporting the existence of regional and global stock markets linkages and provide a comparison of such mul- tivariate GARCH models on the data sample. We find out that the estimated time-varying conditional correlations indicate limited integration among the mar- kets which implies that investors can benefit from the risk reduction by investing in the different stock markets especially during the crisis. Keywords: multivariate GARCH, VECH, BEKK, O-GARCH, GO-GARCH, CCC, DCC
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Solvency Internal models
Mertl, Jakub ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee) ; Jedlička, Petr (referee)
Title: Solvency Internal models Author: Mgr. Ing. Jakub Mertl Abstract: The subject of thesis is assessment of calculation methods on capital adequacy of currently implemented regulation in insurance industry called Solvency II. The aim of the thesis is to build up a partial internal model fulfilling the condition of Solvency II. The thesis deals with the premium and reserve risks that are essential part of non-life business. Different approaches of risk assessment are described and aggregation of those risks as well. An important part of the thesis is a numerical example illustrating presented methods.
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