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Traditional and modern approaches to pricing in nonlife insurance
Vojtěch, Jonáš ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
Title: Traditional and modern approaches to pricing in nonlife insurance Abstract: This thesis deals with the theory and implementation of generalized linear models in the area of pricing of non-life insurance and subsequent optimalization of rates. Using the generalized linear models it is possible to estimate expected value and variance of compound distribution of total claims made according to insurance policy during definite time period. The next step is to build an optimalization model and describe several methods how to determine rates that lead to optimal distribution of safety margins within insurance policies in particular risk groups. Represented approaches how to calculate insurance premiums are numerically illustrated on simulated data in concluding parts of the thesis.
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Mathematical Programming Models for Optimal Control Problems
Dražka, Jan ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
This thesis deals with optimization of a vehicle’s (racing) drive on a track. The model of a vehicle and a track is built in this thesis. The first chapter is devoted to the fastest pass problem formulation. The problem optimizes (in the least time) the vehicle’s drive from a start line to a finish line. The problem is formulated as an optimal control theory problem. In the second chapter the optimal control theory problem is suitably discretised and transformed into a nonlinear programming problem. The transformation of the fastest pass problem into nonlinear programming problem, its detailed and illustrative derivation and reformulation form the main part of the thesis. Third chapter presents the implementation and solution of the problem using GAMS and MATLAB. This thesis is a part of a specific research project on which the author has participated. The main contribution of the author is an original formulation of the fastest pass problem as a nonlinear programming problem and its implementation and solving using GAMS.
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Mathematical Model for Faculty Budget
Holá, Lucie ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
The idea of this diploma thesis is an origin application of optimization models to solve a wage funds allocation problem on various institutes of each faculty. This diploma thesis includes an outline of linear programming models, nonlinear programming models, multiply programming models and parametric programming models. Studied questions are debating in wider context of distributing financial resources from the Budget of the Czech republic, through Ministry of education, youth and sports, universities, faculties after as much as various institutes. The accent is given on question of definition assessment scales of achievement criteria with general-purpose kvantification.
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Process Optimization
Vilém, Jan ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This bachelor's thesis examine the problem of the process optimization in mechanical engineering. It contains optimization model to optimize cutting conditions in turning. The problem was programmed in the GAMS system as linear and nonlinear problem. Limiting conditions are generally defined for several types of technological processes.
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Optimization in Engineering Design
Hrabec, Dušan ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
The aim of present work is to show possibilities of optimization for special basic examples of engineering design. The discussed models have been implemented in GAMS and the corresponding calculations have been performed. The knowledge of linear and non-linear programming is utilized.
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Financial optimization
Štolc, Zdeněk ; Kuncová, Martina (advisor) ; Kalčevová, Jana (referee)
This thesis is focused on a theoretical explanation of some models for the optimization stock portfolios with different risk measure. The theory of the nonlinear programming is detailed developed and also basic Markowitz`s model with another optimization models as Konno -- Yamazaki`s model, Roy`s model, semivariance approach and Value at Risk approach, which are based on alternative risk measure. For all models the assumptions of their applications are highlighted and the comparation of these models is made too. Analytical part is concerned in the construction of the effecient portfolios according to the described models is made on the historical market prices of 13 companies traded on Prague Stock Exchange in SPAD.
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Optimalizační server NEOS
Tabach, Arnošt ; Jablonský, Josef (advisor) ; Kalčevová, Jana (referee)
Tato práce se zabývá využitím serveru NEOS při optimalizačních výpočtech. Jejím cílem je ?ověřit možnosti serveru NEOS a předvést praktické možnosti, zejména pro potřeby výuky. ?Omezuje se na spojení serveru NEOS s optimalizačním systémem AMPL. Obojí je teoreticky ?popsáno v první části, v druhé jsou obsaženy praktické ukázky výpočtů. V závěru jsou stručně ?rozebrány výhody a úskalí při využití serveru NEOS. ?
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