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Causality in multiple time series
Kusenda, Ondrej ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
The bachelor thesis describes causality in multiple time series. Mul- tiple time series are formulated by using vector autoregressive models (VAR). The general properties of the VAR model are defined in the thesis . Model cre- ation involves VAR order selection, estimation of its parameters and checking the properties of the VAR model. The basic concepts of the Granger and instan- taneous Granger causality and theorems for the classification of these relations are defined in the thesis. Tests for the Granger and instantaneous Granger causality are described on suitable models. Subsequently, theoretical knowledge is applied to real data, which are available in the database in the program R. The practical part of the bachelor thesis is performed in the program R. 1
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Difference and differential equations in life insurance
Kirešová, Katarína ; Kříž, Pavel (advisor) ; Pešta, Michal (referee)
The diploma thesis deals with the calculation of life insurance reserves, higher mo- ments and the distribution function of future payments of reserves using difference and differential equations. In the beginning, the basic theory of a stochastic process, insu- rance model, cash flow, and reserve is summarized. After that, equations themselves are derived; first in general and then for four specific types of insurance. Subsequently, a cal- culation of premiums is presented for each type of insurance. The next two chapters deal with the calculation of higher moments and the distribution function. After deriving the formulas for four types of insurance, the reserves, standard deviations, and distribution functions are calculated for specific values and then they are compared with the Monte Carlo simulation. The conclusion contains pros and cons of the method compared to the simulation. 1
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Gradual change model
Míchal, Petr ; Hlávka, Zdeněk (advisor) ; Pešta, Michal (referee)
The thesis aims at change-point estimation in gradual change models. Methods avail- able in literature are reviewed and modified for point-of-stabilisation (PoSt) context, present e.g. in drug continuous manufacturing. We describe in detail the estimation in the linear PoSt model and we extend the methods to quadratic and Emax model. We describe construction of confidence intervals for the change-point, discuss their interpre- tation and show how they can be used in practice. We also address the situation when the assumption of homoscedasticity is not fulfilled. Next, we run simulations to calculate the coverage of confidence intervals for the change-point in discussed models using asymp- totic results and bootstrap with different parameter combinations. We also inspect the simulated distribution of derived estimators with finite sample. In the last chapter, we discuss the situation when the model for the data is incorrectly specified and we calculate the coverage of confidence intervals using simulations. 1
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Technical reserves of non-life insurance in the internal solvency models
Thomayer, Jiří ; Mertl, Jakub (advisor) ; Pešta, Michal (referee)
Title: Technical reserves of non-life insurance in the internal solvency model Author: Bc. Jiří Thomayer Department: Department of Propability and Mathematical Statistics Supervisor: Mgr. Ing. Jakub Mertl Abstract: In this work we study and describe calculation of solvency capital using the standard formula contained in the Directive of the European Union (Solvency II), which should be put into practice in Europe on 1 January 2013. This calcu- lation is described in quantitative impact study 5. We describe a general approach to risk measurement and we show some particular practical measures used to risk measurement. We explain under what conditions the standard formula or its parts can be replaced by internal model. Next, we show disadvantages of using the stan- dard formula and we propose possible internal model to calculate risk premiums and risk reserves in non-life insurance. Finally we apply the proposed model for calculation risk reverses in non-life insurance in practice. Keywords: Standard formula, Risk measurement, Solvency II, Internal model;
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Logistic regression with applications in financial sector
Bílková, Kristýna ; Branda, Martin (advisor) ; Pešta, Michal (referee)
In this bachelor thesis binary logistic regression model is described. Its parameters are estimated by maximum likelihood method. Newton-Raphson's algorithm is used for enumeration of these estimates. There are defined some statistics for testing the significance of the coefficients. Then stepwise regression is desribed. For assessing the quality of the model Pearson's Chi Square Test and Hosmer-Lemeshow's Test of the goodness of fit are defined. Diversification abilitz of the model is illustrated bz the Loreny curve and is quantificated by Gini coefficient, Kolmogorov-Smirnov statistics and generalized coefficient of determination. The theoretical knowledge is applied to insurance area data.
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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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Parametrizace rozdělení škod v neživotním pojištení
Špaková, Mária ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
Title: Parameterization of claims distribution in non-life insurance Author: Bc. Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta Ph.D., MFF UK Abstract: This paper deals with the parameterization of claim size distributions in non-life insurance. It consists of the theoretical and the practical part. In the first part we discuss the usual distributions of claims and their properties. One section is devoted to extreme values distributions. Consequently, we mention the most known methods for parameter estimation - the maximum likelihood method, the method of moments and the method of weighted moments. The last theoretical chapter is focused on some validation techniques and goodness-of-fit tests. In the practical part we apply some of the discussed approaches on real data. However, we concentrate mainly on the large claims modeling - firstly, we select a reasonable threshold for our data and then we fit the claims by the generalized Pareto distribution together with the introduced parameterization procedures. Based on the results of the applied validation methods we will choose appropriate models for the biggest claims. Keywords: parameterization, non-life insurance, claims distribution.
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Operational risk loss distributions
Krajňák, Tomáš ; Mazurová, Lucie (advisor) ; Pešta, Michal (referee)
Operational risk in recent years has become an important part of banks, insurance companies and financial institutions. The proposed work deals with the distributions that best fit the loss severity from the operational risk and also describe their basic properties. Specifically, deals with the g-h distribution, its properties, moments, parameter estimations and tail behavior. There is also another method for high threshold estimation described in this text, the POT (Peaks over threshold). In conclusion, there is the procedure for estimating quantiles of g-h distribution by POT method presented including simulation example in which there are quantile values estimated using the POT method compared to the g-h distribution quantiles.
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Structural Equation Modeling
Kuzminskaya, Kseniya ; Pešta, Michal (advisor) ; Lachout, Petr (referee)
Structural Equation Models (SEM) - also called Simultaneous Equation Models - are used to describe relationships among a set of variables. Similarly as in multivariate regression models, some of the variables are treated as predictors and the others as outcomes. However, unlike in a classical regression model, a variable, which is outcome in one equation, can become a predictor in another equation. SEM are even able to handle variables, which are not measured directly but only through their effects. They are often used in econometrics or socio-economics.
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