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Parametric risk modelling in assessing mortality
Hlavandová, Radana ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
In this thesis we focus on modeling stochastic mortality and parameter risk in assessing mortality. We explore two mortality stochastic models for modeling the number of deaths in portfolio which consist of one or more than one cohort. We define the term mixture of distributions and introduce Beta-Binomial and Poisson-Gamma model. We address immediate life annuities and we apply Bayesian Poisson- Gamma model to quantify longevity risk on data. The obvious increasing trend of average lifetime leads insurance companies to greater protection against longevity risk. We show how to deal with solvency rules by internal models designed consistently with the requirement in the standard formula of Solvency II. Powered by TCPDF (www.tcpdf.org)
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Proportional reinsurance
Kubišová, Barbora ; Mazurová, Lucie (advisor) ; Branda, Martin (referee)
This thesis deals with the issue of proportional reinsurance. It describes the basic types of proportional reinsurance, Quota Share, Surplus and their modi- fications, Variable Quota Share and Table of Lines Surplus. Furthermore, the paper explains how reinsurance changes aggregate claim amounts in the indivi- dual risk model. In this thesis we introduce two criteria for finding optimal ratio of proportional reinsurance. First, the de Finetti's criterion which minimizes the variance of the result of the insurer subject to a given level for the expected re- sult. Second is the optimality criterion which minimizes the (conditional) value at risk of total costs of the insurance company. Finally, we present numerical examples where on the basis of optimality criteria we find the optimal quota, respectively optimal retention level of the reinsurance. 1
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Market consistent valuation of insurance liabilities
Šindelář, Jakub ; Hejmová, Barbora (advisor) ; Branda, Martin (referee)
Market-consistent actuarial valuation of insurance liabilities is important approach not only for regulatory framework Solvency II but also generally for financial and actuarial modeling in insurance companies. It is the reason why we will focus on derivation of basic theory for valuation of cash flow from insurance liabilities by real world probability measure with deflators and risk neutral measure with bank account numeraire (also called equivalent martingale measure). We will show on illustrative examples ekvivalence of both approaches. Further, we will focus on spot rate modeling using discrete time Vasicek model. We use discrete time Vasicek model in Valuation Portfolio theory, where we are trying to replicate insurance liabilities by financial instruments. In theory and also example we use important assumption about independent decoupling of financial events and insurance technical events for theirs modeling.
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Vertex coloring algorithms in scheduling problems under uncertainty
Hájek, Štěpán ; Branda, Martin (advisor) ; Lavička, Karel (referee)
This thesis concerns solutions to problems that arise in optimizing fixed interval scheduling under situations of uncertainty such as when there are random delays in job process times. These problems can be solved by using a vertex coloring with random edges and problems can be formulated using integer linear, quadratic and stochastic programming. In this thesis is propo- sed a new integer linear formulation. Under certain conditions there is proved its equivalence with stochastic formulation, where is maximized the schedule reliability. Moreover, we modified the proposed formulation to obtain bet- ter corresponding to real life situations. In a numerical study we compared computational time of individual formulations. It turns out that the propo- sed formulation is able to solve scheduling problems considerably faster than other formulations. 1
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Insurance pricing methods based on risk measures
Malá, Kateřina ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
In this thesis we study various risk measures and one of their characteristics - the coherence. We talk especially about value-at-risk (VaR in short), respectively about conditional value-at- risk (CVaR). We also mention the advantage of CVaR against VaR. After that we discuss the most common forms of compound distribution that are used in practice. The final part of this bachelor thesis is dedicated to a numerical study where we calculate mean, variance, VaR a CVaR for specific values of parameters.
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Šikmost v teorii optimalizace a eficience portfolia
Mikulík, Petra ; Branda, Martin (advisor) ; Lachout, Petr (referee)
In this thesis we study models, which search for an optimal portfolio from a set of stocks. On the contrary to the classical approach focusing only on expected return and variance, we examine models where an additional crite- rion of skewness is included. Furthermore we formulate a model for measuring performance of a portfolio defined as the distance from the Pareto efficient frontier. In numerical experiments we apply the models on historical prices and stock data from the electronic stock market NASDAQ. We analyze the stock data from companies listed in the index NASDAQ-100. We conclude by comparing of optimal portfolios created using different models among each other, with trivial single-stock portfolios and the with NASDAQ-100 index itself.
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Public Image of Spain Based on Travel Literature Published in 17th - 18th c. England
Branda, Martin ; Klusáková, Luďa (advisor) ; Křížová, Markéta (referee)
The aim of this thesis is to analyze and interpret English travel accounts from 17th and 18th century concerning Spain. One of the texts is original English work, while the other was translated from French. Both of them were available to the contemporary English reader. The thesis analyzes these travel accounts and aims to define the image of Spain and its inhabitants, based on the data from both works. The main goal of this thesis is then to reconstruct the mental map of each traveller, based on the method of cognitive mapping. At the same time, the perceiving of the space, border and the concrete rating of places visited, is also stressed. The next objective of this work is to compare both travel accounts, or propose two different views of Spain during a given time span. Keywords: Image of Spain, travel accounts, Catherine Aulnoy, Robert Southey, mental map
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Diversification in Data Envelopment Analysis in finance
Macková, Simona ; Branda, Martin (advisor) ; Hurt, Jan (referee)
Title: Diversification in Data Envelopment Analysis in Finance Author: Simona Macková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Martin Branda, Ph.D., Department of Probability and Ma- thematical Statistics Abstract: This thesis deals with an extension of data envelopment analysis and its application in finance. This method enables to evaluate the efficiency of cho- sen production units based on several inputs and outputs. Administrative fees or risk measures can be used as inputs and expected incomes of observed assets as outputs in financial application. We show basic traditional models in a form of a primary problem of linear programming and a dual problem as well and later compare with diversification models. It is suitable to deal with diversification which enables to consider dependencies between assets in case of finance and in- vestments. Than we get to nonlinear programming problem hence we introduce appropriate risk and return measures to make the problem solvable. Especially, we focus on the conditional value at risk. Next we introduce the model which deals with diversification. We use this on real data of chosen mutual funds. Keywords: Data envelopment analysis, Efficiency, Diversification, Conditional value at risk
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Scenario trees in stochastic programming problems
Malá, Alena ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multi-stage stochastic linear programming and its ap- plictions in the portfolio selection problem. It presents several models of invest- ment planning, the emphasis is on the basic model with transaction costs and risk adjusted model for every investment level. Random returns entering the above models are modelled by the scenario trees which are generated using the moment- matching method. The thesis presents the optimal investment strategy for each model. It then examines distance of optimal values of objective functions in de- pendence on the nested distance of these generated trees. All calculations were performed using Mathematica software version 9. 1
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Modeling dependencies in claims reserving
Kaderjáková, Zuzana ; Pešta, Michal (advisor) ; Branda, Martin (referee)
The generalized linear models (GLM) lately received a lot of attention in modelling the insurance data. However, the violation of assumptions about the independence of underlying data set often causes problems and misinterpretation of achieved results. The need for more exible instruments has been spoken out and consequently various proposals have been made. This thesis deals with GLM based techniques enabling to handle correlated data sets. The usage have been made of generalized linear mixed models (GLMM) and generalized estimating equations (GEE). The main aim of this thesis is to provide a solid statistical background and perform a practical application to demonstrate and compare features of various models. Powered by TCPDF (www.tcpdf.org)
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