Skip to main content

A Differential Equations Analysis of Stock Prices

  • Conference paper
  • First Online:
Economic and Financial Challenges for Eastern Europe

Abstract

Stock price analysis is one of the most important issues concerning investments and financial decision-making. Thus, stock price analysis and estimation models can be very useful in the estimation of a firm’s financial development. The aim of this paper is to propose a model of differential equations that will be able to be applied in the case of stock price analysis and estimation. The differential equations model will be based on Lanchester’s combat model, a mathematical theory of war. In the field of business, such operations research models have been used in cases such as competition analysis and resources allocation optimization. The case to be examined in this paper refers to the healthcare services index stocks of the Athens Stock Exchange. A 7 × 7 differential equations model was developed to analyze the examined firms’ stocks.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

  • Ballings, M., Van den Poel, D., Hespeels, N., & Gryp, R. (2015). Evaluating multiple classifiers for stock price direction prediction. Expert Systems with Applications, 42(20), 7046–7056.

    Article  Google Scholar 

  • Chalikias, M., & Skordoulis, M. (2016). Implementation of F.W. Lanchester’s combat model in a supply chain in duopoly: The case of Coca-Cola and Pepsi in Greece. Operational Research: An International Journal, 17(3), 737–745. https://doi.org/10.1007/s12351-016-0226-0.

    Article  Google Scholar 

  • Chalikias, M., Lalou, P., & Skordoulis, M. (2016a). Modeling advertising expenditures using differential equations: The case of an oligopoly data set. International Journal of Applied Mathematics and Statistics, 55(2), 23–31.

    Google Scholar 

  • Chalikias, M., Lalou, P., & Skordoulis, M. (2016b). Modeling a bank data set using differential equations: The case of the Greek banking sector. In Proceedings of 5th International Symposium and 27th National Conference of HEL.O.R.S on Operation Research (pp. 113–116). Piraeus, June 2016. Piraeus: Piraeus University of Applied Sciences.

    Google Scholar 

  • Diacogiannis, G. (1996). The usefulness of share prices and inflation for corporate failure prediction. SPOUDAI, 46(3–4), 135–156.

    Google Scholar 

  • Glezakos, M., Merika, A., & Georga, P. (2008). The measurement of share price volatility in the Athens Stock Exchange. SPOUDAI, 58(1–2), 11–30.

    Google Scholar 

  • Hsu, C. M. (2011). A hybrid procedure for stock price prediction by integrating self-organizing map and genetic programming. Expert Systems with Applications, 38(11), 14026–14036.

    Google Scholar 

  • ICAP Group. (2016). Leading sectors of the Greek economy. Athens: ICAP Group.

    Google Scholar 

  • Kim, D. K., & Kil, R. M. (2013). Stock price prediction based on a network with Gaussian Kernel functions. In International Conference on Neural Information Processing (pp. 705–712). Berlin: Springer.

    Google Scholar 

  • Kyriakides, G., Talattinis, K., Kyrmanidou, M., Ioulianou, M., & Stephanides, G. (2016). Assessing the predictive ability of a market’s order book. A study on sports bet exchange. In Proceedings of 5th International Symposium and 27th National Conference of HEL.O.R.S on Operation Research (pp. 138–142). Piraeus, June 2016. Piraeus: Piraeus University of Applied Sciences.

    Google Scholar 

  • Mantegna, R. N. (1999). Hierarchical structure in financial markets. The European Physical Journal B-Condensed Matter and Complex Systems, 11(1), 193–197.

    Article  Google Scholar 

  • Martikainen, T. (1991). Modelling stock price behaviour by financial ratios. Studies in Financial Modelling, 12(1), 119–138.

    Article  Google Scholar 

  • Niarchos, A., & Alexakis, C. (2000). The predictive power of macroeconomic variables on stock market returns. The case of the Athens stock exchange. SPOUDAI, 50(1–2), 75–86.

    Google Scholar 

  • Park, K., & Shin, H. (2013). Stock price prediction based on a complex interrelation network of economic factors. Engineering Applications of Artificial Intelligence, 26(5), 1550–1561.

    Article  Google Scholar 

  • Preethi, G., & Santhi, B. (2012). Stock market forecasting techniques: A survey. Journal of Theoretical & Applied Information Technology, 46(1), 24–30.

    Google Scholar 

  • Shi, S., Liu, W., & Jin, M. (2012, November). Stock price forecasting using a hybrid ARMA and BP neural network and Markov model. In 2012 IEEE 14th International Conference on Communication Technology (ICCT) (pp. 981–985). IEEE.

    Google Scholar 

  • Spilioti, S. N. (2016). Does the sentiment of investors explain differences between predicted and realized stock prices? Studies in Economics and Finance, 33(3), 403–416.

    Article  Google Scholar 

  • Yang, J. W., & Parwada, J. (2012). Predicting stock price movements: An ordered Probit analysis on the Australian Securities Exchange. Quantitative Finance, 12(5), 791–804.

    Article  Google Scholar 

  • Zhang, X. D., Li, A., & Pan, R. (2016). Stock trend prediction based on a new status box method and AdaBoost probabilistic support vector machine. Applied Soft Computing, 49, 385–398.

    Article  Google Scholar 

  • Zhou, J., Bai, T., Zhang, A., & Tian, J. (2008a). The integrated methodology of wavelet transform and GA based-SVM for forecasting share price. In International Conference on Information and Automation, 2008 (pp. 729–733). ICIA 2008. IEEE.

    Google Scholar 

  • Zhou, J., Bai, T., & Suo, C. (2008b). The SVM optimized by culture genetic algorithm and its application in forecasting share price. In IEEE International Conference on Granular Computing, 2008 (pp. 838–843). GrC 2008. IEEE.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Katsouleas, G., Chalikias, M., Skordoulis, M., Sidiropoulos, G. (2019). A Differential Equations Analysis of Stock Prices. In: Sykianakis, N., Polychronidou, P., Karasavvoglou, A. (eds) Economic and Financial Challenges for Eastern Europe. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-12169-3_23

Download citation

Publish with us

Policies and ethics