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Scenario structures in multistage stochastic programs
Harcek, Milan ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multi-stage stochastic programming in the context of random process representation. Basic structure for random process is a scenario tree. The thesis introduces general and stage-independent scenario tree and their properties. Scenario trees can be also combined with Markov chains which describe the state of the system and determine which scenario tree should be used. Another structure which enables reduce the complexity of the problem is a scenario lattice. Scenario generation is performed using moment method. Scenario trees are used for representation of random returns as the input to the investment problem.
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Scenario structures in multistage stochastic programs
Harcek, Milan ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multi-stage stochastic programming in the context of random process representation. Basic structure for random process is a scenario tree. The thesis introduces general and stage-independent scenario tree and their properties. Scenario trees combined with Markov chains are also introduced. Markov chains states determine if there is a crisis period or not. Information about historical number of crises helps us to construct a scenario lattice. Scenario generation is performed using moment method. Scenario trees are used as an input to the investment problem.
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Scenario structures in multistage stochastic programs
Harcek, Milan ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multi-stage stochastic programming in the context of random process representation. Basic structure for random process is a scenario tree. The thesis introduces general and stage-independent scenario tree and their properties. Scenario trees can be also combined with Markov chains which describe the state of the system and determine which scenario tree should be used. Another structure which enables reduce the complexity of the problem is a scenario lattice. Scenario generation is performed using moment method. Scenario trees are used for representation of random returns as the input to the investment problem.
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Stochastic programming problems with chance constraints
Harcek, Milan ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
The thesis presents stochastic programming with chance contraints. We begin with the definition of convex set, convex and concave function and we study the convexity of programs with deterministic constraints. We continue with the definition of quasi-concave and quasi-convex function. After that, we put our mind to probabilistic constraints and the convexity of feasible set and show the formulation of joint and separate probabilistic constraints. We discuss properties of feasible set in general case, without any assumptions concerning the probability distribution of random variable. Finally, we apply our theory to random vectors with finite discrete distribution and multiva- riate normal distribution. 1
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