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Heterogeneous agent models
Vošvrda, Miloslav ; Vácha, Lukáš
The Efficient Markets Hypothesis provides a theoretical basis for trading rules. Fundamentalists rely on their model employing fundamental information basis to forecasting of the next price period. The traders determine whether current conditions call for the acquisition of fundamental information in a forward looking manners, rather than relying on past performance.
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Notes on approximation of stochastic programming problem
Šmíd, Martin
In stochastic optimization problems, expectation of random function is often being minimized. Since the expectation can rarely be evaluated exactly an approximation has to be done. In the present paper, three types of approximation are dealt with: discretization, Monte Carlo and Quasi Monte Carlo. Convergence rate of the approximation error is evaluated and some upper bounds of the error are given.
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Stochastic optimization problems and dependent data
Kaňková, Vlasta
It is well-known that empirical estimates are usually employed when it is necessary to solve a stochastic decision problem depending on a completely unknown probability measure. The aim of this paper is to recall and summarize some rather new results achieved for dependent data that correspond rather often to economic activities.
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Models of 2D point processes applied to analysis of random sums
Volf, Petr
The contribution deals with the compound (cumulative) random process, i.e. the sequence of random increments at random moments. The process is modeled as a 2D point process (or 2D random counting measure), via the intensities of both components. The study starts from the case of compound Poisson process and generalizes to the cases when the components depend on each other, and also on a set of covariates. An example deals with the sequence of financial transactions.
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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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Model and analysis of heterogeneity of random sums
Volf, Petr
The contribution studies a stochastic process which cumulates random increments at random moments, the cumulative process. We deal with the models and statistical analysis of the heterogeneity factors influencing both the intensity of increments and their magnitudes. We propose the estimates of these heterogeneities and we evaluate corresponding probability distributions. An application dealing with the process of financial transactions is solved.
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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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