|
|
Zpětná alokace diversifikačního efektu v pojistném riziku
Kyseľová, Soňa ; Středová, Marcela (advisor) ; Mazurová, Lucie (referee)
The determination of the sufficient amount of economic capital and its allocation to the business lines is the key issue for insurance companies. In this thesis we introduce two methods of aggregating economic capital. One is based on linear correlation and the second deals with copulas. A multitude of allocation principles have been proposed in the literature. We choose those which are the most used in practice and compare advantages and disadvantages of their application. The last chapter is devoted to the numerical examples of capital aggregation and allocation principles. 1
|
|
|
Multivariate Dependence Modeling using Copulas
Klaus, Marek ; Šopov, Boril (advisor) ; Gapko, Petr (referee)
Multivariate volatility models, such as DCC MGARCH, are estimated under assumption of multivariate normal distribution of random variables, while this assumption has been rejected by empirical evidence. Therefore, the esti- mated conditional correlation may not explain the whole dependence struc- ture, since under non-normality the linear correlation is only one of the de- pendency measures. The aim of this thesis is to employ a copula function to the DCC MGARCH model, as copulas are able to link non-normal marginal distributions to create corresponding multivariate joint distribution. The copula-based MGARCH model with uncorrelated dependent errors permits to model conditional cor- relation by DCC-MGARCH and dependence by the copula function, sepa- rately and simultaneously. In other words the model aims to explain addi- tional dependence not captured by traditional DCC MGARCH model due to assumption of normality. In the empirical analysis we apply the model on datasets consisting primarily of stocks of the PX Index and on the pair of S&P500 and NASDAQ100 in order to compare the copula-based MGARCH model to traditional DCC MGARCH in terms of capturing the dependency structure. 1
|
|
|
Advanced Techniques of Risk Aggregation
Dufek, Jaroslav ; Justová, Iva (advisor) ; Pešta, Michal (referee)
In last few years Value-at-Risk (Var) is a very popular and frequently used risk measure. Risk measure VaR is used in most of the financial institutions. VaR is popular thanks to its simple interpretation and simple valuation. Valuation of VaR is a problem if we assume a few dependent risks. So VaR is estimated in a practice. In presented thesis we study theory of stochastic bounding. Using this theory we obtain bounds for VaR of sum a few dependent risks. In next part of presented thesis we show how we can generalize obtained bounds by theory of copulae. Then we show numerical algorithm, which we can use to evaluate bounds, when exact analytical evaluate isn't possible. In a final part of presented thesis we show our results on practical examples.
|
|
|
Model-based evolutionary optimization methods
Bajer, Lukáš ; Holeňa, Martin (advisor) ; Brockhoff, Dimo (referee) ; Pošík, Petr (referee)
Model-based black-box optimization is a topic that has been intensively studied both in academia and industry. Especially real-world optimization tasks are often characterized by expensive or time-demanding objective functions for which statistical models can save resources or speed-up the optimization. Each of three parts of the thesis concerns one such model: first, copulas are used instead of a graphical model in estimation of distribution algorithms, second, RBF networks serve as surrogate models in mixed-variable genetic algorithms, and third, Gaussian processes are employed in Bayesian optimization algorithms as a sampling model and in the Covariance matrix adaptation Evolutionary strategy (CMA-ES) as a surrogate model. The last combination, described in the core part of the thesis, resulted in the Doubly trained surrogate CMA-ES (DTS-CMA-ES). This algorithm uses the uncertainty prediction of a Gaussian process for selecting only a part of the CMA-ES population for evaluation with the expensive objective function while the mean prediction is used for the rest. The DTS-CMA-ES improves upon the state-of-the-art surrogate continuous optimizers in several benchmark tests.
|
|
|
Eventive objects after "have" and "take" - identification and translation correspondences
Křístková, Jana ; Brůhová, Gabriela (advisor) ; Čermák, Jan (referee)
The present MA thesis is concerned with an English verbonominal construction, which consists of a semantically light verb, in the case of the present thesis have and take, with an eventive object. The construction represents one semantic unit, which is proved by a paraphrase in which the object replaces the whole construction as the verb of the clause without any change of meaning. The construction affects the aspectual features of the verb, which is reflected in Czech translation equivalents. It also allows for easier modification and quantification. The kind of determiner and modifier present has an impact on the Czech counterparts, most importantly on the aspect of the verb. Modifiers usually translate as adverbials or adjectives modifying a syntactic object, if the Czech counterpart is verbonominal. The integration of the English modifiers into the Czech sentence is often problematic. The thesis presents a theoretical survey of information on the topic and provides a linguistic description of 279 examples of the construction obtained through the online corpora InterCorp. The examples are analyzed with respect to determiners, quantifiers and modifiers. This, along with the Czech counterparts, is the basis for conclusions on the influence of the construction on the translation to Czech.
|
|
|
Cyber risk modelling using copulas
Spišiak, Michal ; Teplý, Petr (advisor) ; Baruník, Jozef (referee)
Cyber risk or data breach risk can be estimated similarly as other types of operational risk. First we identify problems of cyber risk models in existing literature. A large dataset consisting of 5,713 loss events enables us to apply extreme value theory. We adopt goodness of fit tests adjusted for distribution functions with estimated parameters. These tests are often overlooked in the literature even though they are essential for correct results. We model aggregate losses in three different industries separately and then we combine them using a copula. A t-test reveals that potential one-year global losses due to data breach risk are larger than the GDP of the Czech Republic. Moreover, one-year global cyber risk measured with a 99% CVaR amounts to 2.5% of the global GDP. Unlike others we compare risk measures with other quantities which allows wider audience to understand the magnitude of the cyber risk. An estimate of global data breach risk is a useful indicator not only for insurers, but also for any organization processing sensitive data.
|
|
|
Model-based evolutionary optimization methods
Bajer, Lukáš ; Holeňa, Martin (advisor) ; Brockhoff, Dimo (referee) ; Pošík, Petr (referee)
Model-based black-box optimization is a topic that has been intensively studied both in academia and industry. Especially real-world optimization tasks are often characterized by expensive or time-demanding objective functions for which statistical models can save resources or speed-up the optimization. Each of three parts of the thesis concerns one such model: first, copulas are used instead of a graphical model in estimation of distribution algorithms, second, RBF networks serve as surrogate models in mixed-variable genetic algorithms, and third, Gaussian processes are employed in Bayesian optimization algorithms as a sampling model and in the Covariance matrix adaptation Evolutionary strategy (CMA-ES) as a surrogate model. The last combination, described in the core part of the thesis, resulted in the Doubly trained surrogate CMA-ES (DTS-CMA-ES). This algorithm uses the uncertainty prediction of a Gaussian process for selecting only a part of the CMA-ES population for evaluation with the expensive objective function while the mean prediction is used for the rest. The DTS-CMA-ES improves upon the state-of-the-art surrogate continuous optimizers in several benchmark tests.
|
|
|
Aggregate loss models with dependent frequency and severity
Čápová, Petra ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
In non-life insurance, the independence between the number and size of claims is usually assumed. However, this thesis shows that the assumption of independence can be omitted. We deal with the dependency modeling between frequency and severity of claims. For including the dependence to the total claims model, we consider two methods. The first method uses generalized linear models and the second method used in the thesis is based on dependence modeling by copulas. We also perform a model with independent frequency and severity of claims. This model is compared with the described methods in the simulation part of the thesis. We include dependency on explanatory (rating) variables in all of these models. 1
|
|
|
Statistical inference in multivariate distributions based on copula models
Kika, Vojtěch ; Omelka, Marek (advisor) ; Hlubinka, Daniel (referee)
Diploma thesis abstract Thesis title: Statistical inference in multivariate distributions based on copula models Author: Vojtěch Kika This diploma thesis aims for statistical inference in copula based models. Ba- sics of copula theory are described, followed by methods for statistical inference. These are divided into three main groups. First of them are parametric methods for copula parameter estimation which assume fully parametric structure, thus for both joint and marginal distributions. The second group consists of semi- parametric methods for copula parameter estimation which, unlike parametric methods, do not require parametric structure for marginal distributions. The last group describes goodness-of-fit tests used for testing the hypothesis that consi- dered copula belongs to some specific copula family. The thesis is accompanied by a simulation study that investigates the dependence of the observed coverage of the asymptotic confidence intervals for copula parameter on the sample size. Pseudolikelihood method was chosen for the simulation study since it is one of the most popular semiparametric methods. It is shown that sample size of 50 seems to be sufficient for the observed coverage to be close to the theoretical one. For Frank and Gumbel-Hougaard copula families even sample size of 30 gives us...
|
|
|
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)
|
guest ::
