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Prediction error in non-life claims reserves
Divišová, Kateřina ; Justová, Iva (advisor) ; Mandl, Petr (referee)
This thesis deals with a description of three claims reserving methods - with stochastic models for Chain ladder, Bornhuetter/Ferguson and multiplicative method. There are mentioned their assumptions, parameter estimates, their properties and formulas for loss reserves in the first part. The second part of the text is devoted to formulas for the mean squared error of prediction and its estimate. Finally, a numerical example shows comparison of these methods.
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Non-life Underwriting Risk in Solvency II - Undertaking Specific Parameters
Šimková, Barbora ; Justová, Iva (advisor) ; Mazurová, Lucie (referee)
of the bachelor's thesis Title: Non-life Underwriting Risk in Solvency II - Undertaking Specific Parameters Author: Barbora Šimková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ing. Iva Justová Ph.D. Abstract: The thesis deals with methods by which it is possible to calculate specific estimate of standard deviation of risk in non-life premium risk. Premium risk is the risk caused by lack of insurance, when the undertaking does not have sufficient cover for future losses. Calculation methods are based on static methods and they comprise the knowledge taught at MFF UK. The thesis analyzes methods of calculating specific parameters and it explains how to calculate capital requirement for non-life premium and reserve risk; capital requirement reflects parameters of risk. An assessment of cap- ital requirements that uses specific parameters for an undertaking is in conclusion of the thesis. The evaluation is performed on a group of insurance companies from dif- ferent countries that used replacement of specific parameters in the calculation of risk premiums in Solvency II. Keywords: non-life underwriting risk, Solvency II, undertaking specific parameters
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Asymptotic Control of Portfolio for several assets
Kováč, Jakub ; Dostál, Petr (advisor) ; Justová, Iva (referee)
We consider an investor who invests in a stock and money market and whose goal is to maximize the market value of her portfolio in the very long run. The goal of the thesis is to find an optimal trading strategy for the investor. The stocks' market values are simulated by multidimensional Brownian motion. The possibility to buy and sell stocks introduces a new dimension to the dynamics of the problem. By using the Itoo calculus we derive the basic properties of the continous model. Considering the continous model difficulties with finding the optimal trading strategy, we aproximate the continous model by a dsicrete model. In the end, the thesis presents hints to use the Howard algorithm in the discrete case. The main contribution of the thesis is the introduction and proof of the Howard algorithm which can be used as a tool to find the optimal trading strategy in the discrete model.
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Capital requirements for insurance companies under Solvency II and its quantification
Kožár, Martin ; Pleška, Martin (advisor) ; Justová, Iva (referee)
This thesis studies project Solvency II, which is focused on the integrated regulation of insurance market in the European Union. It presents basic division and capital requirements arising from it. It describes division of the project into the three areas, refered to as pillars in practice. The thesis summarizes the basic methods for measuring the risk (Value at Risk, Tail Value at Risk), necessary in the calculation of the solvency capital requirements. The thesis studies the method of calculation of the solvency capital requirement SCR and the minimum capital requirement MCR. The calculation of the SCR is focused mainly on the method of the calculation of the capital requirement using the standard formula. Lastly, capital requirements are calculated using concrete data set.
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