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Market Graph and Markowitz Model
Ch. 15. P. 301–313.
Market graph is known to be a useful tool for market network analysis. Cliques and independent sets of the market graph give an information about con- centrated dependent sets of stocks and distributed independent sets of stocks on the market. In the present paper the connections between market graph and classical Markowitz portfolio theory are studied. In particular, efficient frontiers of cliques and independent sets of the market graph are compared with the efficient frontier of the market. The main result is: efficient frontier of the market can be well ap- proximated by the efficient frontier of the maximum independent set of the market graph constructed on the sets of stocks with the highest Sharp ratio. This allows to reduce the number of stocks for portfolio optimization without the loss of quality of obtained portfolios. In addition it is shown that cliques of the market graphs are not suitable for portfolio optimization.
In book
NY: Springer, 2014.
ЦЫГАНКОВА Е. П., Koldanov P., В кн.: Математическое и компьютерное моделирование в экономике, страховании и управлении рисками: сборник статей. Выпуск 10. Материалы XIV Научно-практической конференции. Саратов, 20–22 ноября 2025 г.Вып. 10.: Саратов: Саратовский университет, 2025.
The task of analyzing the dynamics of the market graph is to determine whether the observed changes in the market graph are systematic or if such changes can be explained by random fluctuations in correlation estimates on the market. The work proposes a test for detecting market graph dynamics and a procedure for constructing a ...
Added: July 20, 2026
Koldanov A. P., Koldanov P., Semenov D., Журнал Новой экономической ассоциации 2025 № 1(66) С. 54–74
The problem of connections’ analysis between the stock returns is considered. The connections are measured by traditional Pearson correlation as well as rank Kendall correlation. Different measures of uncertainty conclusions on connections in the stock markets based on separation of the conclusions by significant and admissible are proposed. The proposed measures of uncertainty include the ...
Added: December 3, 2024
Semenov D., Koldanov A. P., Koldanov P. et al., Annals of Mathematics and Artificial Intelligence 2024
In this paper we propose a new notion of a clique reliability. The clique reliability is understood as the ratio of the number of statistically significant links in a clique to the number of edges of the clique. This notion relies on a recently proposed original technique for separating inferences about pairwise connections between vertices ...
Added: January 30, 2024
Semenov D., Alexander Koldanov, Petr Koldanov, Computational Management Science 2024 Vol. 21 Article 18
The aim of the article is to analyze graphs of weakly correlated stocks. Characteristics
of these graphs such as number of edges, histogram of vertices degrees, degrees
distribution, hubs and cliques are investigated. Pearson correlation and Kendall correlation
are used to construct these graphs. Graphs constructed by the traditional
procedure and by Holm procedure are compared. Obtained results are ...
Added: January 24, 2024
Shabanov D. A., Шайхеева Т. М., Математические заметки 2020 Т. 107 № 3 С. 454–465
This paper deals with list colorings of uniform hypergraphs. Let H(m, r, k) be the complete r-partite k-uniform hypergraph with parts of equal size m in which each edge contains exactly one vertex from some k ≤ r parts. Using results on multiple covers by independent sets, we establish that, for fixed k and r, ...
Added: June 14, 2020
Kazakov M., Kalyagin V. A., , in: Models, Algorithms and Technologies for Network Analysis, Springer Proceedings in Mathematics & StatisticsVol. 156.: Switzerland: Springer, 2016. P. 135–156.
Random matrix theory (RMT) is applied to investigate the cross-correlation matrix of a financial time series in four different stock markets: Russian, American, German, and Chinese. The deviations of distribution of eigenvalues of market correlation matrix from RMT global regime are investigated. Specific properties of each market are observed and discussed. ...
Added: October 14, 2018
Sirotkin D., Malyshev D., Discrete Mathematics and Applications 2018 Vol. 28 No. 4 P. 249–258
The independent set problem for a given simple graph is to determine the size of a maximal set
of its pairwise non-adjacent vertices. We propose a new way of graph reduction leading to a new proof of
the NP-completeness of the independent set problem in the class of planar graphs and to the proof of NPcompleteness of ...
Added: August 22, 2018
Kalyagin V. A., Koldanov A. P., Koldanov P. et al., Annals of Operations Research 2018 Vol. 266 No. 1-2 P. 313–327
Research into the market graph is attracting increasing attention in stock market analysis. One of the important problems connected with the market graph is its identification from observations. The standard way of identifying the market graph is to use a simple procedure based on statistical estimations of Pearson correlations between pairs of stocks. Recently a ...
Added: May 17, 2017
fgh g., Salohodjaev R., Environmental Research 2016 Vol. 147 P. 82–88
This paper investigates the determinants of nations' commitment to environmental protection at the international level by focusing on the role of national intelligence and the level of democracy. The national intelligence is measured by nation's IQ scores. The findings based on a sample of 152 nations provide strong evidence that intelligence has statistically significant impact ...
Added: October 21, 2016
San Segundo P., Nikolaev A., Batsyn M. et al., Informatica 2016 Vol. 27 No. 2 P. 463–487
This paper improves an infra-chromatic bound which is used by the exact branch-and-bound maximum clique solver BBMCX (San Segundo et al., 2015, Computers & Operations Research, p. 293-303) as an upper bound on the clique number for every subproblem. The infra-chromatic bound looks for triplets of color subsets which cannot contain a 3-clique. As a ...
Added: September 16, 2016
Kalyagin V. A., Koldanov A. P., Petr A. Koldanov, Journal of Statistical Planning and Inference 2017 Vol. 181 No. Feb P. 30–40
A class of distribution free multiple decision statistical procedures is proposed for threshold graph identification in correlation networks. The decision procedures are based on simultaneous application of sign statistics. It is proved that single step, step down Holm and step up Hochberg statistical procedures for threshold graph identification are distribution free in sign similarity network in ...
Added: December 14, 2015
Koldanov A. P., Kalyagin V. A., Pardalos P. M., Lecture Notes in Computer Science 2015 Vol. 9432 P. 26–36
Stock selection by Sharp ratio is considered in the framework of multiple statistical hypotheses testing theory. The main attention is paid to comparison of Holm stepdown and Hochberg step up procedures for different loss functions. Comparison is made on the basis of condittional risk as a function of selection threshold. This approach allows to discover ...
Added: December 13, 2015
Koldanov P., Комиссарова А. Э., , in: Models, Algorithms, and Technologies for Network Analysis / From the 4th International Conference on Network Analysis.: NY: Springer, 2016. P. 157–163.
The paper deal with uncertainty in market network analysis. The main problem addressed is to investigate statistical uncertainty of Kruskal algorithm for the minimum spanning tree in market network. Uncertainty of Kruskal algorithm is measured by the probability of q incorrectly included edges. Numerical experiments are conducted with the returns of a set of 100 ...
Added: December 7, 2015
Bautin G. A., Koldanov A. P., Pardalos P. M., Springer Optimization and Its Applications 2014 Vol. 100 P. 25–33
Financial market can be modeled as network represented by a complete weighted graph. Differet characteristics of this graph (minimum spanning tree, market graph ad others) give an impotant information on the network. In the pesent paper it is studied how the choice of measure of similarity between stocks influences the statistical errors in the calculation ...
Added: October 13, 2014
Koldanov P., Pardalos P. M., Zamaraev V. A., , in: DATA ANALYTICS 2014, The Third International Conference on Data Analytics.: [б.и.], 2014. P. 91–94.
A common network representation of the stock market is based on correlations of time series of return fluctuations. It is well known that financial time series have a stochastic nature. Therefore there is uncertainty in inference about filtered structures in market network. Thus market network analysis need to be complemented by estimation of uncertainty of the ...
Added: October 13, 2014
Kalyagin V. A., Koldanov P., Zamaraev V. A., Springer Optimization and Its Applications 2014 Vol. 100 P. 181–197
Network model of stock market based on correlation matrix is considered. In the model vector of stock returns is supposed to hve multivariate normal distribution with given correlation matrix. Statistical uncertainty of some popular market network structures is analyzed by numerical simulation for network models of stock makets for different countries. For each market statistical ...
Added: October 13, 2014