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MCMC metody ve výpočetní statistice a ekonometrii
Volf, Petr
The paper recals the MCMC methods, namely the Gibbs algorithm, the Metropolis--Hastings algorithm and variants used for solution of optimization problems, namely the simulated annealing. The objective is to describe the schemes of the algorithms, to recall their theoretical foundation, and to show their use both in Bayes data analysis and in randomized optimization problem.
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Porovnání aproximací v úlohách stochastické a robustní optimalizace
Houda, Michal
The paper deals with two wide areas of optimization theory: stochastic and robust programming. We specialize to different approaches when solving an optimization problem where some uncertainties in constraints occur. To overcome uncertainty, we can request the solution to be feasible to all but a small part of constraints. Both approaches gives us different methods to deal with this requirement. We try to find fundamental differencies between them and illustrate the differencies on a simple numerical example.
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Optimální strategie na trhu s limitními objednávkami
Šmíd, Martin
We define a decision problem of an investor, trading continuously at a limit order market, maximizing a utility from his wealth at a random time horizon. We show that, in special cases (e.g. risk neutrality, quadratic or exponential utility function), the problem may be factorized and, given additional restrictions, it may even be solved.
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Markovská vlastnost trhu s limitními objednávkami
Šmíd, Martin
We formulate a rigorousmathematical description of a limit order market (we describe the state of the market by means of atomic measures). Further, we state sufficient conditions for the evolution of the market to be Markov; in particular, all the agents should either trade randomly or use strategies dependent only on the current state of the market and on external random elements.
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Úlohy stochastického programování s lineární kompensací: Aplikace na problematiku dvou manažérů
Kaňková, Vlasta
Stochastic programming problems with recourse are a composition of two (outer and inner) optimization problems. A solution of the outer problem depends on the "underlying" probability measure while a solution of the inner problem depends on the solution of the outer problem and on the random element realization. Evidently, a position and optimal behaviour of two managers can (in many cases) be described by this type of the model in which an optimal behaviour of the main manager is determined by the outer problem while the optimal behaviour of the second manager is described by the inner problem. We focus on an investigation of the inner problem.
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Aproximace stochastických a robustních optimalizačních úloh
Houda, Michal
The paper deals with two wide areas of optimization theory: stochastic and robust programming. We specialize to different approaches when solving an optimization problem where some uncertainties in constraints occur. To overcome uncertainty, we can request the solution to be feasible to all but a small part of constraints. Both approaches gives us different methods to deal with this requirement. We try to find fundamental differencies between them and illustrate the differencies on a simple numerical example.
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Empirické procesy ve stochastickém programování
Kaňková, Vlasta ; Houda, Michal
Usually, it is very complicated to investigate and to solve optimization problems depending on a probability measure. To this end a stability of them, considers with respect to a prabability measure space, has been discused in the stochastic programming literature many times. The paper is focus on the investigation of the stability with respect to the Wasserstein and to the Komolgorov metrics with "underlying" L_1 space. Moreover, we applay achieved stability results to empirical estimates.
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