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Problems of Stochastic Optimisation under Uncertainty, Quantitative Methods, Simulations, Applications in Gas Storage Valuation
Omelčenko, Vadim ; Kaňková, Vlasta (advisor) ; Ortobelli, Sergio (referee) ; Popela, Pavel (referee)
This dissertation deals with heavy-tailed distributions and the problematics of stochastic dominance for stable distributions. In terms of stochastic dominance in the setup of stable distributions, we prove novel results which are mostly based on the domain of attraction of stable distributions. We introduce a bivariate sub-family of stable distributions, which can easily be simulated and used for the joint modelling of dependent data (such as spot and forward prices). The marginals of these bivariate distributions are stable and can have a different tail index. We also present our approach for parameter estimation of stable distributions. The theoretical results achieved are used for the valuation of gas storage units. In this part of the dissertation, we use stochastic dynamic programming to address this problem, and we present several algorithms.
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Problems of Stochastic Optimisation under Uncertainty, Quantitative Methods, Simulations, Applications in Gas Storage Valuation
Omelčenko, Vadim ; Kaňková, Vlasta (advisor) ; Ortobelli, Sergio (referee) ; Popela, Pavel (referee)
This dissertation deals with heavy-tailed distributions and the problematics of stochastic dominance for stable distributions. In terms of stochastic dominance in the setup of stable distributions, we prove novel results which are mostly based on the domain of attraction of stable distributions. We introduce a bivariate sub-family of stable distributions, which can easily be simulated and used for the joint modelling of dependent data (such as spot and forward prices). The marginals of these bivariate distributions are stable and can have a different tail index. We also present our approach for parameter estimation of stable distributions. The theoretical results achieved are used for the valuation of gas storage units. In this part of the dissertation, we use stochastic dynamic programming to address this problem, and we present several algorithms.
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Maximum likelihood estimators and their approximations
Tyuleneva, Anastasia ; Omelčenko, Vadim (advisor) ; Zvára, Karel (referee)
Title: Maximum likelihood estimators and their approximations Author: Anastasia Tyuleneva Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Vadym Omelchenko Abstract: Maximum likelihood estimators method is one of the most effective and accurate methods that was used for estimation distributions and parameters. In this work we will find out the pros and cons of this method and will compare it with other estimation models. In the theoretical part we will review important theorems and definitions for creating common solution algorithms and for processing the real data. In the practical part we will use the MLE on the case study distributions for estimating the unknown parameters. In the final part we will apply this method on the real price data of EEX A. G, Germani. Also we will compare this method with other typical methods of estimation distributions and parameters and chose the best distribution. All tests and estimators will be provided by Mathematica software. Keywords: parametr estimates, Maximum Likelihood estimators, MLE, Stable distribution, Characteristic function, Pearson's chi-squared test, Rao-Crámer. .
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