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An Alternative Approach to the Structure Determination of Hierarchical Archimedean Copulas
Górecki, J. ; Holeňa, Martin
Copulas offer very a flexible tool for a stochastic dependence modeling. One of the most popular classes of copulas is the class of hierarchical Archimedean copulas, which gained its popularity due to the fact that the models from the class are able to model the stochastic dependencies conveniently even in high dimensions. One critical issue when estimating a hierarchical Archimedean copula is to correctly determine its structure. The paper describes an approach to the problem of the structure determination of a hierarchical Archimedean copula, which is based on the close relationship of the copula structure and the values of measure of concordance computed on all its bivariate margins. The presented approach is conveniently summarized as a simple algorithm.
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Fuzzy Methods in Land Use Modeling for Archaeology
Machálek, T. ; Cimler, R. ; Olševičová, K. ; Danielisová, Alžběta
The general objective of our research is to develop the complex agentbased simulation of ancient Celtic society population, food production and economics. To achieve this we proposed the agent-based agricultural model of land suitability for miscellaneous farming systems. The behaviour of agents is controlled by a fuzzy rule-based system. The system encodes farmers' agricultural knowledge as regards the decision where to apply specific farming method. Corresponding linguistic variables describe (1) the distance of individual land patches from the household, (2) the slope of the land, (3) the yield of individual land patches and (4) total harvest as a percentage of inhabitants' annual nutritional requirement. To prevent high-frequency spatial changes in land suitability caused by time-dependent stochastic nature of the crop yields, our model performs result smoothing using spatial signal filtering.
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On quantile optimization problem with censored data
Volf, Petr
In the framework of stochastic optimization the criterion based on selected quantiles is considered. Further, stochastic characteristics are estimated from censored data. Therefore, certain theoretical results concerning estimators of distribution function and quantiles under censoring are recalled and utilized to prove consistency of solution based on estimates. Behavior of solutions for finite data sizes is studied with the aid of randomly generated example.
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Economic and Financial Problems via Multiobjective Stochastic Optimization
Kaňková, Vlasta
Multiobjective optimization problems depending on a probability measure correspond to many economic and financial activities. Evidently if the probability measure is completely known, then we can try to influence economic process employing methods of multiobjective deterministic optimization theory. Since this assumption is fulfilled very seldom we have mostly to analyze the mathematical model and consequently also economic process on the data base. The aim of the talk will be to investigate a relationship between ``characteristics" obtained on the base of complete knowledge of the probability measure and them obtained on the above mentioned data base. To this end, the results of the deterministic multiobjective optimization theory and the results obtained for stochastic one objective problems will be employed.
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Portfolio competitions and rationality
Kuběna, Aleš Antonín ; Šmíd, Martin
We study investment competitions in which the players with highest achieved returns are rewarded by fixed prizes. We show that, under realistic assumptions, a game the participants play lacks a pure equilibrium and that the ``max-min'' solution of the game lies in one of the extremal points of the feasible set, namely in the one having maximal probability that the portfolio return falls into its normal cone. We analyse empirically a portfolio competition held recently by the Czech portal ``lidovky.cz''; we find that the majority of people do not behave according to the game-theoretic conclusions. Consequently, searching for factors influencing a choice of particular stocks, we find that that the only significant determinant of the choice is a size of the stock's issuer.
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Cumulative Optimality in Risk-Sensitive and Risk-Neutral Markov Reward Chains
Sladký, Karel
This contribution is devoted to risk-sensitive and risk-neutral optimality in Markov decision chains. Since the traditional optimality criteria (e.g. discounted or average rewards) cannot reflect the variability-risk features of the problem, and using the mean variance selection rules that stem from the classical work of Markowitz present some technical difficulties, we are interested in expectation of the stream of rewards generated by the Markov chain that is evaluated by an exponential utility function with a given risk sensitivity coefficient. Recall that for the risk sensitivity coefficient equal zero we arrive at¨traditional optimality criteria. In this note we present necessary and sufficient risk-sensitivity and risk-neutral optimality conditions; in detail for unichain models and indicate their generalization to multichain Markov reward chains.
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