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A note on the use of copulas in chance-constrained programming
Houda, Michal
In this paper we are concentrated on a problem of linear chanceconstrained programming where the constraint matrix is considered random with a known distribution of the matrix rows. The rows are not considered to be independent; instead, we make use of the copula notion to describe the dependence of the matrix rows. In particular, the distribution of the rows is driven by so-called Archimedean class of copulas. We provide a review of very basic properties of Archimedean copulas and describe how they can be used to transform the stochastic programming problem into a deterministic problem of second-order cone programming. Also the question of convexity of the problem is explored and importance of the selected class of copulas is commented. At the end of the paper, we provide a simple example to illustrate the concept used.
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Multiobjective Stochastic Optimization Problems with Probability Constraints
Kaňková, Vlasta
Rather general multiobjective optimization problems depending on a probability measure correspond often to situations in which an economic or financial process is simultaneously influenced by a random factor and a “decision” parameter; moreover simultaneously it is reasonable to evaluate the process by a few objective functions and it seems reasonable to determine the decision with to the mathematical expectation of objectives. A complete knowledge of the probability measure is a necessary assumption to analyze the problem. However, in applications mostly the problem has to be solved on the data base. A relationship between “characteristics” obtained on the base of complete knowledge of the probability measure and them obtained on the above mentioned data base has been already investigated in the case when constraints are not depending on the probability measure. The aim of the talk will be to relax this condition.
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Multifactor dynamic credit risk model
Dufek, J. ; Šmíd, Martin
We propose a new dynamic model of the Merton type, based on the Vasicek model. We generalize Vasicek model in three ways: we add model for loss given default (LGD), we add dynamics to the model and we allow non-normal distri- butions of risk factors. Then we add a retrospective interaction of underlying factors and found a non-linear behaviour of these factors. In particular, the evolution of factors underlying the DR and the LGD is assumed to be ruled by a non-linear vector AR process with lagged DR and LGD and their non-linear transformations. We apply our new model on real US mortgage data and demonstrate its statistical significance.
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On Bayes approach to optimization
Volf, Petr
In many real optimization problems we have not full information on the objective function and can afford to evaluate it at just a few points. Then, certain assumptions on the objective function must be done. This could be taken as a prior information in a Bayes scheme. The Bayes approach to optimization then offers the way of effective search for the extremal point. We describe the technique how to mapproach the optimum using the Gauss process or a regression-like models.
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Applying System Dynamics and Agent-based Modelling in Archaeological Simulation
Olševičová, K. ; Danielisová, Alžběta
We apply the social simulation to the cultural milieu of the late Iron Age in Central Europe and its economic strategies, especially on the subsistence and the carrying capacity of the settlement agglomeration in relation to the daily economic needs of its inhabitants. By means of the computational models of the economics of the particular central settlement (Staré Hradisko oppidum) and its hinterland we aim to verify hypotheses about the economic sustainability in case self-supplying is applied. To achieve this, the agent-based modelling, cellular automata approach and system dynamics modelling are used. In the paper we present four alternative scenarios of population dynamics (baseline and three versions of depopulation) and four alternative scenarios of food production and agricultural practices (baseline and three types of external events). The set of models for all scenarios was implemented in NetLogo and Stella. Outputs of the models are subject of interests of archaeologists and according to their feedback the models will be refined and extended.
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Robust Regularized Cluster Analysis for High-Dimensional Data
Kalina, Jan ; Vlčková, Katarína
This paper presents new approaches to the hierarchical agglomerative cluster analysis for high-dimensional data. First, we propose a regularized version of the hierarchical cluster analysis for categorical data with a large number of categories. It exploits a regularized version of various test statistics of homogeneity in contingency tables as the measure of distance between two clusters. Further, our aim is cluster analysis of continuous data with a large number of variables. Various regularization techniques tailor-made for high-dimensional data have been proposed, which have however turned out to suffer from a high sensitivity to the presence of outlying measurements in the data. As a robust solution, we recommend to combine two newly proposed methods, namely a regularized version of robust principal component analysis and a regularized Mahalanobis distance, which is based on an asymptotically optimal regularization of the covariance matrix. We bring arguments in favor of the newly proposed methods.
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