National Repository of Grey Literature 92 records found  1 - 10nextend  jump to record: Search took 0.02 seconds. 
Risk aggregation allowing for skewness
Šimonová, Soňa ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
The main objective of this thesis is to examine different methods of calcula- tion of economic capital for an insurance company which allow for skewness. For calculating the economic capital we use two alternative risk measures- Value at Risk (VaR) and Conditional Value at Risk (CVaR). The first part of the thesis is concerned with deriving exact formulae for VaR and CVaR for normally distribu- ted losses and describing the modification of these formulae using Cornish-Fisher approximation. Next, the method using lognormal model with a parameter cap- turing skewness is discussed. The parameter is used for deriving a formula for skewness of a sum of losses. The approximation of the sum is thus obtained and is used for deriving formulae for VaR and CVaR for aggregated losses. Finally, the methods are compared numerically using R software. 1
Composite distributions of loss sizes
Karatun, Ksenia ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
In this work, we deal with composite distributions that can be used to model loss sizes in some specific classes of non-life insurance. The first part contains definition of the general composite model and its special features. The second part describes models that are made up by piecing together Weibull distribution and distributions belonging to a family of transformed beta distributions. The third part describes algorithm that computes the maximum likelihood estimators for parameters of composite distribution and criteria of the relative quality of statistical models. In the last part we apply composite models to two real data sets. 1
Reverse mortgage
Korotkov, Daniil ; Mazurová, Lucie (advisor) ; Večeř, Jan (referee)
ČSOB Pojišťovna, a. s., člen holdingu ČSOB Veřejné 1 / 1 20.7.2018 Abstract: At this moment, reverse mortgages are relatively new products on the Czech market and this thesis deals with their problematics. In this thesis, we describe the main risks related to reverse mortgages, namely, longevity risk and adverse evolution of property prices. Analyzing these risks we are modelling the underlying property prices, their future behavior, discount factors along with studying the risk models such as vector autoregression, hedonic model, repeat-sales and Wills-Sherris model. In practical part, we focus on estimating the parameters of Lee-Carter model and autoregression model of zero-coupon government bond as well as applying the results of the estimation to calculate various characteristics of reverse mortgages.
Risk quantification in annuity insurance
Berdák, Vladimír ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
The thesis examines the impact of individual risks on an annuity product. It focuses on the deffered whole life annuity and on two basic risks, which affect the overall loss the most. These are interest rate risk and longevity risk. We choose standard deviation (σ), value at risk (VaR) and expected shortfall (ES) at different confidence levels for target risk measures. Hoeffding decomposition is used to split the overall loss. Then Euler allocation principle will show the distribution of individual risks for different entry ages.
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.
Risk quantification in annuity insurance
Berdák, Vladimír ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
The thesis examines the impact of individual risks on an annuity product. It focuses on the deffered whole life annuity and on two basic risks, which affect the overall loss the most. These are interest rate risk and longevity risk. We choose standard deviation (σ), value at risk (VaR) and expected shortfall (ES) at different confidence levels for target risk measures. Euler allocation principle and Hoeffding decomposition are used to split the overall loss. These methods will show the distribution of individual risks for different entry ages.
Truncated data and stochastic claims reserving
Marko, Dominik ; Pešta, Michal (advisor) ; Mazurová, Lucie (referee)
In this thesis stochastic claims reserving under the model of randomly trun- cated data is presented. For modelling the claims, a compound Poisson process is assumed. Introducing a random variable representing the delay between oc- currence and reporting of a claim, a probability model of IBNR claims is built. The fact that some claims are incurred but not reported yet leads to truncated data. Basic results of non-parametric statistical estimation under the model of randomly truncated data are shown, which can be used to obtain an estimate of IBNR claims reserves. Theoretical background is then used for application on real data from Czech Insurers' Bureau. 36
Modelling dependent lives
Pavčová, Eva ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
Title: Modelling Dependent Lives Author: Eva Pavčová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis, we model the dependence between the remaining lifetimes of a husband and wife using a specific Markov model. We examined the impact of the dependence on the net single premium using the specific Markov model that captures the long-term dependence between lifetimes of the two considered lives. Using this model we have calculated 10-year joint-life annuity due and 10-year last-survivor annuity due considering the age rage (37, 80) in case of dependence and also independence of the two considered lives. The calculations were based on the dataset related to the Czech population in 2015. The impact of the dependence between the remaining lifetimes of the husband and wife was found to be not significant. Keywords: positive quadrant depedence, multiple life insurance premiums, depen- dent lifetimes, joint-life annuity, last-survivor annuity, joint-life and last-survivor models
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
Random rates of return in financial and insurance mathematics
Pejic, Mladen ; Zichová, Jitka (advisor) ; Mazurová, Lucie (referee)
Title: Random rates of return in financial and insurance mathematics Author: Mladen Pejic Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathema- tical Statistics Abstract in English language: The thesis is focused on the study of stochastic life annuities. It represents a combination of basic probability with financial mathe- matics and life insurance. The first part is focused on financial mathematics. Special attention is paid to the calculation of present and future values of annui- ties with stochastic interest rates. In the second part, we demonstrate the use of random interest rates in calculations of present values of annuities related to life insurance. In the third part, we focus on the application of log - normal distribu- tion, which is mostly used in real life problems. In the last part, a numerical study is presented. We asses the effect of the log - normal distribution parameters on the present value of the annuities and we examine the accuracy of the estimates made by the method of moments. ii

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1 Mazurová, Lenka
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