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Risk models of annuity damages in non-life insurance Šmarda, Tomáš ; Zimmermann, Pavel (advisor) This thesis is focused on practical application of two methods used in non-life insurance, Nested Monte Carlo and Least squares Monte Carlo. Best estimate and 99.5% quantile was calculated using both methods and results was compared. Both methods are similar in estimates and therefore can be used for computation of capital requirement. Least squares Monte Carlo seem more favourable, because it significantly reduces computation time. Detailed record

Mathematical modeling of gold price ŠMARDA, Tomáš This bachelor thesis is focused on mathematical modelling of gold price. After introducing basic models of Box-Jenkins methodology and models of conditional hetoskedasticity, the time series was modelled by random walk process. The time series has not constant variance, neither normal distribution, therefore for the second model was considered volatility model GARCH. Using the volatility model GARCH is possible to refine prediction intervals for forecast one step ahead. Results were calculated in R software and MS Excel. Detailed record

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2	ŠMARDA, Tomáš

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