Skip to main content
SpringerLink
Log in

A Pseudo-Boolean Approach to the Market Graph Analysis by Means of the p-Median Model

  • Chapter
  • First Online:
Clusters, Orders, and Trees: Methods and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 92))

Abstract

In the course of recent 10 years algorithms and technologies for network structure analysis have been applied to financial markets among other approaches. The first step of such an analysis is to describe the considered financial market via the correlation matrix of stocks prices over a certain period of time. The second step is to build a graph in which vertices represent stocks and edge weights represent correlation coefficients between the corresponding stocks. In this paper we suggest a new method of analyzing stock markets based on dividing a market into several substructures (called stars) in which all stocks are strongly correlated with a leading (central, median) stock. Our method is based on the p-median model a feasible solution to which is represented by a collection of stars. Our reduction of the adjusted p-Median Problem to the Mixed Boolean pseudo-Boolean Linear Programming Problem is able to find an exact optimal solution for markets with at most 1,000 stocks by means of general purpose solvers like CPLEX. We have designed and implemented a high-quality greedy-type heuristic for large-sized (many thousands of stocks) markets. We observed an important “median nesting” property of returned solutions: the p leading stocks, or medians, of the stars are repeated in the solution for p + 1 stars. Moreover, many leading stocks (medians), for example, in the USA stock market are the well-known market indices and funds such as the Dow Jones, S&P which form the largest stars (clusters).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Mantegna, R.N.: Hierarchical structure in financial markets. Eur. Phys. J. B 11, 193–197 (1999)

    Article  Google Scholar 

  2. Kullmann, L., Kertesz, J., Mantegna, R.N.: Identification of clusters of companies in stock indices via Potts super-paramagnetic transactions. Physica A 287, 412–419 (2000)

    Article  Google Scholar 

  3. Onnela, J.-P., Chakraborti, A., Kaski, K., Kertesz, J.: Dynamic asset trees and portfolio analysis. Eur. Phys. J. B 30, 285–288 (2002)

    Article  MathSciNet  Google Scholar 

  4. Onnela, J.-P., Chakraborti, A., Kaski, K., Kertesz, J., Kanto, A.: Asset trees and asset graphs in financial markets. Phys. Scr. T106, 48–54 (2003)

    Article  MATH  Google Scholar 

  5. Cukur, S., Eryigit, M., Eryigit, R.: Cross correlations in an emerging market financial data. Physica A 376, 555–564 (2007)

    Article  Google Scholar 

  6. Onnela, J.-P., Chakraborti, A., Kaski, K., Kertesz, J.: Dynamic asset trees and Black Monday. Physica A 324, 247–252 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kenett, D.Y., Shapira, Y., Madi, A., Bransburg-Zabary, S., Gur-Gershgoren, G., Ben-Jacob, E.: Dynamics of stock market correlations. AUCO Czech Econ. Rev. 4, 330–340 (2010)

    Google Scholar 

  8. Kenett, D.Y., Tumminello, M., Madi, A., Gur-Gershgoren, G., Mantegna, R.N.: Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market. PLoS ONE 12(5), 1–14 (2010)

    Google Scholar 

  9. Boginski, V., Butenko, S., Pardalos, P.M.: Statistical analysis of financial networks. Comput. Stat. Data Anal. 48, 431–443 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Boginski, V., Butenko, S., Pardalos, P.M.: Mining market data: a network approach. Comput. Oper. Res. 33, 3171–3184 (2006)

    Article  MATH  Google Scholar 

  11. Jung, W.-S., Chae, S., Yang, J.-S., Moon, H.-T.: Characteristics of the Korean stock market correlations. Physica A 361, 263–271 (2006)

    Article  Google Scholar 

  12. Huang, W.-Q., Zhuang, X.-T., Yao, S.: A network analysis of the Chinese stock market. Physica A 388, 2956–2964 (2009)

    Article  Google Scholar 

  13. Tabak, B.M., Serra, T.R., Cajueiro, D.O.: Topological properties of stock market networks: the case of Brazil. Physica A 389, 3240–3249 (2010)

    Article  Google Scholar 

  14. Jallo, D., Budai, D., Boginski, V., Goldengorin, B., Pardalos, P.M.: Network-based representation of stock market dynamics: an application to American and Swedish stock markets. Springer Proc. Math. Stat. 32, 91–108 (2013)

    Google Scholar 

  15. Reese, J.: Solution methods for the p-Median problem: an annotated bibliography. Networks 48(3), 125–142 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mladenovic, N., Brimberg, J., Hansen, P., Moreno-Perez, J.A.: The p-median problem: a survey of metaheuristic approaches. Eur. J. Oper. Res. 179, 927–939 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hammer, P.L.: Plant location - a pseudo-Boolean approach. Isr. J. Technol. 6, 330–332 (1968)

    MATH  Google Scholar 

  18. Beresnev, V.L.: On a problem of mathematical standardization theory. Upravliajemyje Sistemy 11, 43–54 (1973) [in Russian]

    Google Scholar 

  19. AlBdaiwi, B.F., Ghosh, D., Goldengorin, B.: Data aggregation for p-median problems. J. Comb. Optim. 3(21), 348–363 (2011)

    Article  MathSciNet  Google Scholar 

  20. AlBdaiwi, B.F., Goldengorin, B., Sierksma, G.: Equivalent instances of the simple plant location problem. Comput. Math. Appl. 57(5), 812–820 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  21. Goldengorin, B., Krushinsky, D.: Complexity evaluation of benchmark instances for the p-median problem. Math. Comput. Model. 53, 1719–1736 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  22. Goldengorin, B., Krushinsky, D., Slomp, J.: Flexible PMP approach for large size cell formation. Oper. Res. 60(5), 1157–1166 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  23. Goldengorin, B., Krushinsky, D., Pardalos, P.M.: Cell Formation in Industrial Engineering. Theory, Algorithms and Experiments. Springer, Berlin, 218 pp. (2013). ISBN:978-1-4614-8001-3

    Google Scholar 

  24. Bekker, H., Braad, E.P., Goldengorin, B.: Using bipartite and multidimensional matching to select the roots of a system of polynomial equations. In: Computational Science and Its Applications—ICCSA. Lecture Notes in Computer Science, vol. 3483, pp. 397–406. Springer, Berlin (2005)

    Google Scholar 

  25. Goldengorin, B., Krushinsky, D.: A computational study of the pseudo-Boolean approach to the p-median problem applied to cell formation. In: Pahl, J., Reiners, T., Voß, S. (eds.) Network Optimization: Proceedings of 5th International Conference (INOC 2011), Hamburg, 13-16 June 2011. Lecture Notes in Computer Science, vol. 6701, pp. 503–516. Springer, Berlin (2011)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Operations Department, Faculty of Economics and Business, University of Groningen, Nettelbosje 2, 9747 AE, Groningen, The Netherlands

    Boris Goldengorin

  2. Center of Applied Optimization, University of Florida, 401 Weil Hall, 116595, Gainesville, FL, 32611-6595, USA

    Boris Goldengorin & Panos M. Pardalos

  3. Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics, 136 Rodionova, Nizhny Novgorod, Russian Federation

    Anton Kocheturov

Authors
  1. Boris Goldengorin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anton Kocheturov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Panos M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Boris Goldengorin .

Editor information

Editors and Affiliations

  1. Department of Higher Mathematics, National Research University Higher School of Economics, Moscow, Russia

    Fuad Aleskerov

  2. Department of Operations, University of Groningen, Groningen, The Netherlands

    Boris Goldengorin

  3. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Goldengorin, B., Kocheturov, A., Pardalos, P.M. (2014). A Pseudo-Boolean Approach to the Market Graph Analysis by Means of the p-Median Model. In: Aleskerov, F., Goldengorin, B., Pardalos, P. (eds) Clusters, Orders, and Trees: Methods and Applications. Springer Optimization and Its Applications, vol 92. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0742-7_5

Download citation

Publish with us

Policies and ethics

Search

Navigation