
Seasonal mortality and its application in life insurance
Srnáková, Andrea ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
Assumptions like uniform distribution, constant force of mortality and the Balducci assumption frequently used for modeling mortality data do not reflect the variability of monthly death rates. Often a phenomenon of winter excess mortality occurs, which is not respected by these assumptions. We shall apply a seasonal mortality assumption, which uses nonnegative trigonometric sums for modeling the distribution of monthly death rates. We then apply our findings to the Czech mortality data. We calculate monthly premiums in a shortterm life insurance policy and compare the result with results given by the classical assumptions. 1


Counterparty risk in reinsurance
Kohout, Marek ; Cipra, Tomáš (advisor) ; Pešta, Michal (referee)
The main goal of this Bachelor thesis is to present a survey of methods for cal culating the required capital to cover the default risk of reinsurers in the frame work of the regulatory system Solvency II in EU. The methods are based on socalled common shock principle which is preferred in the case of portfolios with a smaller number of heterogeneous counterparties (e. g. reinsurers). In difference from (Hendrych and Cipra, 2018) the case with flexible weights of particular reinsurers given by their LGD (loss given default) is considered. One discusses the results of extensive numerical study comparing particular methods. 1


Moving averages in time series
Uhliarik, Andrej ; Cipra, Tomáš (advisor) ; Hudecová, Šárka (referee)
This thesis focuses on time series analysis usikng methods based on moving averages, especially the method based on the approximation of the trend compo nent of a time series by polynomial functions. In the theoretical part of the thesis, we describe procedures for choosing right weights, degree and length of moving average for a specific time series. In the practical part, we are demonstrating this process on real data. A part of the thesis is a simple software for smoothing time series and tables with weights of moving averages for specific degrees and lengths. 1


Parametric Nonlinearity Testing in Time Series
Kollárová, Dominika ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The aim of this bachelor thesis is the theoretical description of the functioning of two parametric nonlinearity tests  the RESET test and Keenan's test and theirs application on financial time series with the summary of achieved results. During the testing we assume, that a time series follows a predetermined linear AR(p) model the order of which is identified by the partial autocorrelation function or the AIC criterion.


Mortality in high ages
Malá, Kateřina ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
In this thesis, we study modelling of mortality in high ages by several approaches. Some of mentioned models take into account the phenomenon of mortality deceleration. Further, we present several ways of estimating of exposed to risk in (almost) extinct cohorts. We focus especially on the survivor ratio method but we also mention the MD method and the DG method. Finally, we perform a numerical study.


Seasonal exponential smoothing
Rábek, Július ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This thesis deals with the issues of time series modeling, where seasonal component is present. Principles of basic seasonal exponential smoothing methods: simple and double exponential smoothing, Holt's method, which are applicable on time series without seasonality, are described in the beginning. For seasonal time series, HoltWinters exponential smoothing is the most suitable method. This method is introduced in both of its versions and the usage of either version depends on the characteristics of the seasonal component. Furthermore, state space modeling is presented as a statistical framework for exponential smoothing methods, joined with a discussion of some selected problems related with practical implementation of these techniques together with suggestions of their solution. Finally, HoltWinters method on two real data time series with seasonality is presented.


Ensemble learning methods for scoring models development
Nožička, Michal ; Witzany, Jiří (advisor) ; Cipra, Tomáš (referee)
Credit scoring is very important process in banking industry during which each potential or current client is assigned credit score that in certain way expresses client's probability of default, i.e. failing to meet his or her obligations on time or in full amount. This is a cornerstone of credit risk management in banking industry. Traditionally, statistical models (such as logistic regression model) are used for credit scoring in practice. Despite many advantages of such approach, recent research shows many alternatives that are in some ways superior to those traditional models. This master thesis is focused on introducing ensemble learning models (in particular constructed by using bagging, boosting and stacking algorithms) with various base models (in particular logistic regression, random forest, support vector machines and artificial neural network) as possible alternatives and challengers to traditional statistical models used for credit scoring and compares their advantages and disadvantages. Accuracy and predictive power of those scoring models is examined using standard measures of accuracy and predictive power in credit scoring field (in particular GINI coefficient and LIFT coefficient) on a real world dataset and obtained results are presented. The main result of this comparative study is that...


Reinsurance optimization using stochastic programming and risk measures
Došel, Jan ; Branda, Martin (advisor) ; Cipra, Tomáš (referee)
Title: Reinsurance optimization using stochastic programming and risk measures Author: Jan Došel Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Martin Branda, Ph.D., Department of Probability and Mathe matical Statistics Abstract: The diploma thesis deals with an application of a stochastic progra mming in a reinsurance optimization problem in terms of a present regulatory framework of the insurance companies within the European Union, i.e. Solvency II. In this context, the reinsurance does not only transfer a portion of the risk to the reinsurer but also reduces an amout of required capital. The thesis utilizes certain risk measures and their properties, premium principles and nonlinear in teger programming. In the theoretical part, there are basic terms from Solvency II, reinsurance, risk measures and the comonotonicity of random variables descri bed and the optimization problem itself is derived. The approach is then applied in the practical part on data of Czech Insurers' Bureau using the GAMS software. Finally, a stability of the solution is tested depending on several parameters. Keywords: reinsurance optimization, stochastic programming, Solvency II, risk measures 1


Median in some statistical methods
Bejda, Přemysl ; Cipra, Tomáš (advisor) ; Hlávka, Zdeněk (referee) ; Víšek, Jan Ámos (referee)
Median in some statistical methods Abstract: This work is focused on utilization of robust properties of median. We propose variety of algorithms with respect to their breakdown point. In addition, other properties are studied such as consistency (strong or weak), equivariance and computational complexity. From practical point of view we are looking for methods balancing good robust properties and computational complexity, be cause these two properties do not usually correspond to each other. The disser tation is divided to two parts. In the first part, robust methods similar to the exponential smoothing are suggested. Firstly, the previous results for the exponential smoothing with ab solute norm are generalized using the regression quantiles. Further, the method based on the classical sign test is introduced, which deals not only with outliers but also detects change points. In the second part we propose new estimators of location. These estimators select a robust set around the geometric median, enlarge it and compute the (iterative) weighted mean from it. In this way we obtain a robust estimator in the sense of the breakdown point which exploits more information from observations than standard estimators. We apply our approach on the concepts of boxplot and bagplot. We work in a general normed vector...


Median in some statistical methods
Bejda, Přemysl ; Cipra, Tomáš (advisor)
Median in some statistical methods Abstract: This work is focused on utilization of robust properties of median. We propose variety of algorithms with respect to their breakdown point. In addition, other properties are studied such as consistency (strong or weak), equivariance and computational complexity. From practical point of view we are looking for methods balancing good robust properties and computational complexity, be cause these two properties do not usually correspond to each other. The disser tation is divided to two parts. In the first part, robust methods similar to the exponential smoothing are suggested. Firstly, the previous results for the exponential smoothing with ab solute norm are generalized using the regression quantiles. Further, the method based on the classical sign test is introduced, which deals not only with outliers but also detects change points. In the second part we propose new estimators of location. These estimators select a robust set around the geometric median, enlarge it and compute the (iterative) weighted mean from it. In this way we obtain a robust estimator in the sense of the breakdown point which exploits more information from observations than standard estimators. We apply our approach on the concepts of boxplot and bagplot. We work in a general normed vector...
