National Repository of Grey Literature 35 records found  1 - 10nextend  jump to record: Search took 0.01 seconds. 
Likelihood based estimation
Březinová, Eva ; Maciak, Matúš (advisor) ; Kříž, Pavel (referee)
In this thesis we will describe the maximum likelihood method, method of estima- ting unknown parameters that determine the probability distribution of the observed data. We will also introduce other methods derived from the likelihood. We focus pri- marily on a quasi-likelihood and a pseudo-likelihood approach. Then we briefly describe profile likelihood, empirical likelihood, and conditional likelihood. The thesis includes a simulation study which compares the quality of the estimators based on the maximum likelihood and the quasi-likelihood or the maximum likelihood and the pseudo-likelihood using the mean squared error. 1
Approximations of the Aggregate Loss Distribution
Antalicová, Viktória ; Mazurová, Lucie (advisor) ; Kříž, Pavel (referee)
This thesis is focused on the approximation of the distribution of aggregate losses. We first present a method for modelling aggregate losses, which involves selecting an appropriate frequency and severity distributions. Next, the computation of aggregate losses as the sum of the respective number of individual losses is explained. In the sec- ond section, we discuss the approximation of the distribution of the simulated aggregate losses. We present the distributions chosen for the approximation, the method for esti- mating the parameters of these distributions, and the subsequent testing of fit of these distributions with the actual distribution of the simulated aggregate losses. In the third chapter we show the results of this approximation and indicate the suitability of using each of the considered distributions for modelling aggregate losses. In the last section, we introduce the Edgeworth approximation as a method for approximating the distribution of aggregate losses. 1
Additivity of Chain-Ladder method for projection of technical provisions in non-life insurance
Němec, Adam ; Cipra, Tomáš (advisor) ; Kříž, Pavel (referee)
This bachelor thesis deals with the subject of additivity of projections obtained by the Chain Ladder method in the corresponding cumulative development triangles. The reader first gets acquainted with the Chain Ladder method itself and then one presents basic theoretical insights concerning the additivity of projections and the related projection inequality. It also discusses practical interpretation, which it demonstrates us- ing real reinsurance data. Moreover, standard errors of projections in triangles are briefly described in a separate chapter using basic theory of probability and applied in the given numerical study. 1
Distributions of (a,b,0) type in non-life insurance
Zejda, Albert ; Kříž, Pavel (advisor) ; Mazurová, Lucie (referee)
First, a definition of the distribution type (a, b, 0) is introduced. Next, it is shown which known distributions satisfy this definition, the parameters a and b that correspond to them, and specific sets of parameters for each of the distributions are determined. Then, it is proven that no other distributions can satisfy this definition. A maximum likelihood estimation method for estimating the parameters a and b directly from the data is presented. Finally, a simulation study is conducted, in which the probabilities from the estimated distribution type (a, b, 0) from specific data using the maximum likelihood method are compared with the empirical relative frequencies calculated from the data. 1
Superposition and thinning of counting processes in non-life insurance
Romaňák, Martin ; Pešta, Michal (advisor) ; Kříž, Pavel (referee)
The thesis examines a model for representing the number of claims after merging or splitting different lines of business of an insurance company. The model is based on count- ing processes, the Poisson and the renewal processes are considered in particular. The operations of superposition and thinning are the proposed solution to this problem. We present the well-known results that the Poisson processes are closed under superposition and several types of thinning and explore the necessary conditions for this statement to also hold for renewal processes. Specifically, the previous work on the superposition of renewal processes is studied and further clarified, and an original result is derived for two types of thinning of a renewal process. The theoretical results are then used to analyze real insurance data in a model situation when an insurance company wants to estimate the future number of claims after merging two of its lines of business. 1
Claim inflation in car insurance
Neumann, Vojtěch ; Kříž, Pavel (advisor) ; Cipra, Tomáš (referee)
This thesis explores the practical use of generalized linear models. The aim of the thesis is to analyze the claims inflation for Motor Third Party Liability Insurance. For this purpose, current data from a Czech insurance company are provided. In the thesis, a generalized linear model is constructed in detail based on specified criteria. From the model, the effect of inflation is identified and its value for the given period is determined. 1
Parameter estimation for fractional Brownian motion
Hartman, Štěpán ; Kříž, Pavel (advisor) ; Čoupek, Petr (referee)
This bachelor's thesis deals with a mathematical object called fractional Brownian motion, which has substantial applications in a wide variety of disciplines including, next to theoretical and financial mathematics, the fields of biology, geography, or information technology. This concept is a generalization of a standard Brownian motion, in which we do not assume the independence of its increments. In this thesis we define said object and explore its basic properties. Subsequently, we discuss the estimators of its Hurst index. We suggest a correction of one of the methods of constructing the estimator and demonstrate its effectiveness using both simulated and real-life data. 1
Design and verification of an intervention exercise program aimed at improving the fitness of recreational athletes
KŘÍŽ, Pavel
The aim of this work is to compile an intervention program aimed at improving fitness. The goal was achieved. According to the proposal, the intervention exercise program can be practiced by everyone and anywhere, even if the gyms are closed, for example for pandemic reasons. Eleven people took part in the exercise exercise program, and the control group also included eleven people. The EUROFIT test battery, consisting of nine tests, was chosen within the methodology. From the results, it should be emphasized that the experimental group improved on average by 0,1 try for endurance training standing on one leg, 1.89 seconds for tapping, also improved in the overhang in the forward bend by 3.23 centimeters, 13, 96 in the jump from the place, 3.17 repetitions in the sit-ups exercise, 4.79 seconds in the endurance in the squat, the only deterioration of the experimental group occurred in the shuttle run by 0.2 seconds, in the last dynamometry measurement test there was an improvement of 7.14 Newtons. In the control group, there was a slight deterioration in the first test by 0.1 attempts, we could also observe a deterioration in the tapping test by 1.33 seconds, a slight improvement of 0.98 centimeters occurred in the forward bend, the group only further deteriorated in all tests. Specifically, by 0.54 centimeters in the jump, by 0.84 repetitions in the sit-up, 2.56 seconds in the endurance of the push-up, 0.29 in the shuttle run and by 2.23 Newtons in the dynamometry. All research assumptions have been met.
Optimal FInancial Payoffs Maximizing Utility Function
Kožnar, František ; Večeř, Jan (advisor) ; Kříž, Pavel (referee)
The goal of this thesis is to characterize payoffs that maximize expected utility function in different market setups. One can solve this problem in its generality in terms of a function of a likelihood ratio between the subjective measure of an agent P and a risk neutral measure Q. Such payoffs should be transformed to the function of the terminal stock price. The question is what measure P should be chosen, the natural candidates would correspond to either the frequentist or the Bayesian choice of the parameters. The thesis should provide a link to the Kelly Criterion in the binomial evolution of the stock price and to the Merton's Portfolio Problem in the geometric Brownian motion exam- ple showing the possible extensions of these well known problems in the novel Bayesian setup. The thesis should discuss pricing and hedging of these contracts together with their asymptotic behavior. 1
Malliavin operators for real-valued Gaussian random variables and their applications
Kubát, Martin ; Kříž, Pavel (advisor) ; Čoupek, Petr (referee)
In this thesis, we introduce Malliavin Operators. We will focus on derivative, di- vergence and Ornstein-Uhlenbeck operator to study properties of transformed Gaussian random variables. We will explain all concepts in detail and add some typical examples. Then we will use Malliavin operators in the proofs of famous Poincaré inequality and variance expansions. The technique of the last proofs provides a good general approach how to solve similar problems with understanding Malliavin Operators. 1

National Repository of Grey Literature : 35 records found   1 - 10nextend  jump to record:
See also: similar author names
16 KŘÍŽ, Pavel
29 KŘÍŽ, Petr
29 Kříž, Petr
3 Kříž, Petr,
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