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Optimization of building constructions with probability constraints
Kokrda, Lukáš ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with penalty approach to stochastic optimization with chance constraints which are applied to structural mechanics. The problem of optimal design of beam dimensions is modeled and solved. The uncertainty is involved in the form of random load. The corresponding mathematical model contains a condition in the form of ordinary differencial equation that is solved by finite element method. The probability condition is approximated by several types of penalty functions. The results are obtained by computations in the MATLAB software.
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New Trends in Stochastic Programming
Szabados, Viktor ; Kaňková, Vlasta (advisor) ; Lachout, Petr (referee)
Stochastic methods are present in our daily lives, especially when we need to make a decision based on uncertain events. In this thesis, we present basic approaches used in stochastic tasks. In the first chapter, we define the stochastic problem and introduce basic methods and tasks which are present in the literature. In the second chapter, we present various problems which are non-linearly dependent on the probability measure. Moreover, we introduce deterministic and non-deterministic multicriteria tasks. In the third chapter, we give an insight on the concept of stochastic dominance and we describe the methods that are used in tasks with multidimensional stochastic dominance. In the fourth chapter, we capitalize on the knowledge from chapters two and three and we try to solve the role of portfolio optimization on real data using different approaches. 1
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Optimal Value of Loans via Stochastic Programming
Kaňková, Vlasta
A question of mortgage leads to serious and complicated problems of financial mathematics. On one side is a bank with an aim to have a “good” profit, on the other side is the client trying to invest money safely, with possible “small” risk.Let us suppose that a young married couple is in a position of client. Young people know that an expected and also unexpected unpleasant financial situation can happen. Many unpleasant financial situation can be caused by a random factor. Consequently stochastic methods are suitable to secure against them. The aim of the suggested model is not only to state a maximal reasonable value of loans, but also to endure unpleasant financial period. To this end we employ stochastic optimization theory. A few suitable models will be introduced. The choice of the model depends on environment of the young people. Models will be with “deterministic” constraints, probability constraints, but also with stochastic dominance constraints. The suggested models will be analyzed both from the numerical point of view and from possible method solution based on data. Except static one-objective problem we suggest also multi–objective models.
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New Trends in Stochastic Programming
Szabados, Viktor ; Kaňková, Vlasta (advisor) ; Lachout, Petr (referee)
Stochastic methods are present in our daily lives, especially when we need to make a decision based on uncertain events. In this thesis, we present basic approaches used in stochastic tasks. In the first chapter, we define the stochastic problem and introduce basic methods and tasks which are present in the literature. In the second chapter, we present various problems which are non-linearly dependent on the probability measure. Moreover, we introduce deterministic and non-deterministic multicriteria tasks. In the third chapter, we give an insight on the concept of stochastic dominance and we describe the methods that are used in tasks with multidimensional stochastic dominance. In the fourth chapter, we capitalize on the knowledge from chapters two and three and we try to solve the role of portfolio optimization on real data using different approaches. 1
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Optimization of building constructions with probability constraints
Kokrda, Lukáš ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with penalty approach to stochastic optimization with chance constraints which are applied to structural mechanics. The problem of optimal design of beam dimensions is modeled and solved. The uncertainty is involved in the form of random load. The corresponding mathematical model contains a condition in the form of ordinary differencial equation that is solved by finite element method. The probability condition is approximated by several types of penalty functions. The results are obtained by computations in the MATLAB software.
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A Simple Decision Problem of a Market Maker
Šmíd, Martin
We formulate a simple decision model of a market maker maximizing an utility from his consumption. We reduce the dimensionality of the problem to one. We nd that, given our setting, the quotes set by the market maker depend on the inventory of the traded asset but not on the amount of cash held by the market maker.
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