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 Âûïóñê 88
- Agasandyan G. Continuous var-criterion and investor's optimal portfolio
The work investigates the problem of extending the methodology of applying continuous VaR-criterion (CC-VaR) by investors of one-period option markets with one underlier on tasks of constructing the optimal investor’s portfolio for analogical markets with several underliers, i.e., multidimensional markets. The one-period ideal theoretical multidimensional delta-market is defined, and its tools and the algorithm of constructing optimal-on-CC-VaR portfolio of multidimensional delta-instruments by using the Newman – Pearson procedure are formed. In many ways, the algorithm repeats the sequence of operations from the algorithm of the one-dimensional market, but applied to multidimensional objects. The processing of the theoretical algorithm is illustrated by an example of the two-dimensional delta-market, and the optimal solution is searched by analytical methods. The forecast and cost functions, the dissonant, the ordering and weighted functions, and also basic investment performances are calculated. Some singularity presented in the example is eliminated by a natural and rational way and demonstrates possibilities of extending the canonical model. The exposition is illustrated by graphics.
- Zorkaltsev V., Polkovskaya M. Results of the analysis of requirements for methods for allocating time series components
Abstract: The problem of method’s choosing for selecting components of a time series is considered. Such components can be a trend or periodic fluctuations (in particular, seasonal). The studied methods for selecting components are presented as a mapping of the original time series to the selected components. The requirements for these maps have been formulated: continuity, idempotency, additivity, and consideration of the informative nature of observations. In addition, we prove theorems that all the requirements are met by the decomposition into components of a time series using the least squares method. The selection of two components of a time series (trend and seasonal components) from quarterly and monthly data based on an additive model has been considered. The trend is defined as a polynomial of time, and seasonal fluctuations are defined as the sum of strictly periodic functions weighted by degrees of time. The presented additive model is applicable for analyzing the dynamics of stocks, production, transport, consumption of individual products in different areas, etc. It is more appropriate to use a multiplicative model for price dynamics, since indicators measured in relative rather than balance values are more stable. In this case, instead of the additivity requirement discussed in the article, it is necessary to introduce the multiplicativity requirement.
- Gorelov M. On a quantity of information required for efficient control
It is well known that for effective management it is necessary to use information about the surrounding world. But if there is a lot of this information, then one have to save the resources spent on its receipt and processing. Therefore, the question arises of finding rational ways to handle this information. One of the models that allow us to study this question by formal methods is investigated in the article. The simplest control system under risk is considered. It is assumed that information about the realized value of a random factor is available to the operating party. This information is encoded in binary words. The choice of information content, that is, the encoding method, is considered as the prerogative of the operating party. A control result acceptable to the operating party is determined. The task is set to find an encoding method that can guarantee to get this result with the smallest expected value of the length of the message about the realized value of the uncertain factor. It is shown that under very general assumptions this expected value is finite. The qualitative structure of the function from the set of possible values ?of a random factor to the set of binary words, which defines the optimal coding method, is clarified. The task of search such a function is reduced to solving the stochastic programming problem on a “finite-dimensional” space. The results obtained have a reasonable meaningful interpretation. This allows us to conclude that the model constructed correctly reflects the main features of the simulated phenomenon and deserves further study.
- Esin A. Analysis and design principles of modern control systems based on multi-valued logic models
An analysis and an overview of modern applications based on three-valued logic have been presented in this paper. Small computing units based on three-valued logic is a better solution (in comparison with binary models) for several applications such as the telecommunications industry, where three-valued logic units may increase the data transmission rate by one and a half times. It is important to have a possibility to assembly any circuits from three-valued logic chips. An important fundamental problem of class completeness for three-valued logic functions must be solved to make such implementation possible. The class completeness for three-valued logic functions guarantees that any digital circuit may be assembled from the finite number of ternary chipsets. The closure operator on the set of three-valued functions has been considered in this paper. It is a strength of the substitution operator. The completeness problem for this operator has been proved. This fact allows to restore in the general case the sublattice of closed classes with respect to the classical operator of superpositions. It’s a principal theoretical result that can optimize the assembly process for new digital circuits for transmission and data processing problems.
- Sorokin A. Improvement of information-analytical complexes based on hierarchical systems of fuzzy output
Provisions for the improvement of computing systems based on the use of hierarchical fuzzy inference systems associated with preliminary data preparation and subsequent interpretation of the results are proposed. Data preparation is based on performing operations to normalize the input parameter values to a scale with the same range of values, provided that these values have a positive correlation with the values of the output variable. The implementation of the provisions is based on the use of piecewise functions. The use of provisions makes it possible to simplify the formation of production rules in the knowledge base of the fuzzy inference system. The study of the behavior of changes in estimates depending on the number of levels of hierarchies in the computing system made it possible to identify a property associated with the grouping of output estimates in the vicinity of the values of the terms that describe the output variable. This made it possible to refer the hierarchical system of fuzzy inference to the classifier of the analyzed objects by their state, taking into account the criteria of the assessment. Belonging to a certain class is determined by the value of the integral final grade. For the identify groups of objects with similar properties within classes, a set of operations is proposed based on the sequential use of the mountain clustering algorithm, the Euclidean metric and the Hausdorff metric. The use of operations makes it possible to single out typical representatives of the studied classes, and then determine the objects that are closest to them in terms of parameters, taking into account the established restrictions on deviations. The experiment carried out confirmed the efficiency of the proposed provisions.
- Tkachev D. Influence of changing threshold values of proximity index of party’s positions on the measure of the balancedness of the reichstag of the weimar republic
In this research we study 8 convocations of the Weimar Reichstag between 1920 and 1933. For each convocation we construct models, describing all possible coalitions in the Reichstag. The ideology of each party can be identified by their position on the “left/right” scale. Parties of the Reichstag are prescribed the index from 1 to 10 depending on their position on this scale. The index of left parties is close to 1, whereas the index of right parties is close to 10. To evaluate two parties can coalesce we calculate the distance of these parties’ positions on the “left/right” scale, that is equal to the index difference. It is assumed that the high distance of two parties means the impossibility to coalesce. Several models of coalition formation are constructed on the threshold value of positions distance. A parliament is called balanced if it consists of two coalitions. We evaluate the measure of the balancedness, which shows the degree of proximity to the total balanced parliament. We use two different methods to calculate the measure of the balancedness. First one includes all possible coalitions in the Reichstag. The second measure includes only coalitions in which the number of votes is greater than the established quota of the Reichstag convocation. For each model we evaluate the measure of the balancedness using both methods.
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