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Ekonomické procesy a empirická data
Kaňková, Vlasta
Optimizatiom problems depending on a completely unknown probability measure are considered. In particular, there are considered optimization problems with objective functions in a form mathematical expectation of functions depednding on a random parameter. In such situations, usually, an empirical measure replaced the theoretical one. The aim of the paper is to discuss corresponding estimates of the optimal value and optimal solution based on the independent as well as on some types od dependent data.
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Algorithmic procedures for moment optimality in Markovian decision models
Sitař, Milan
We consider a discrete time Markov reward process with finite state and action spaces and random returns. In contrast with the classical models we assume that instead of maximizing the long run average expected return we maximize the first moment and simultaneously minimize the second moment of the reward. An algorithmic procedure is suggested for finding Pareto optimal policies for the considered moment optimality criteria.
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Some remarks on the variance in Markov chains with rewards
Sladký, Karel ; Sitař, Milan
We consider a discrete time Markov reward process with finite state space and assume that the rewards associated with the transitions are random variables with known probability distributions and finite first and second moments. We are interested in properties of cumulative reward earned in the subsequent transitions of the Markov chain. Explicit formulas for expected values and variance of the cumulative (random) reward are obtained for finite and infinite horizon models.
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Poznámka k úlohám vícekriteriální stochastické optimalizace a silně (strongly) konvexním funkcím
Kaňková, Vlasta
Multiobjective problems with an operator of mathematical expectation in objective functions and a constraints set depending (generally) on a probability measure are considered. The aim of the paper is to introduce modified assertions on a stability (considered w.r.t. a propbability measures space) of the (properly) efficient points set and the behaviour of the corresponding empirical estimates. To this end at least one component of the objective functions is supposed to be strongly convex.
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