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On Recurrence Relations and Application in Predicting Price Dynamics in the Presence of Economic Recession

Received: 26 February 2017     Accepted: 27 March 2017     Published: 8 June 2017
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Abstract

Recurrence relations is one of the fundamental Mathematical tools of computation as most computational tasks rely on recursive techniques at one time or the other. In this paper, we present some important theorems on recurrence relations and give more simplified approach of determining an explicit formula for a given recurrence relation subject to specified boundary values (initial conditions). We recursively apply Recurrence Relation technique to model Economic wealth decay as a result of recession. We show both numerical computation and graphical representation of our simple model and analysis of market price dynamics due to Economic recession.

Published in International Journal of Discrete Mathematics (Volume 2, Issue 4)
DOI 10.11648/j.dmath.20170204.12
Page(s) 125-131
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Recurrence Relations (RR), Price Dynamics, Economic Recession

References
[1] M. Crampin, ‘Piecewise linear recurrence relations’, The Mathematical Gazette, 76 (477), 1992, pp. 355–359. doi: 10.2307/3618372.
[2] J. Doyne Farmer, Shareen Joshi. The Price Dynamics of common Trading Strategies. Journal of Economic Behaviour and Organization, Vol. 49 (2002), pp. 149-171.
[3] E. Steven, Discrete Mathematics: Advance counting technique, pp.1-29.
[4] S. Niloufar, Solving linear recurrence relations. http://www.cse.yorku.ca/course_archive/2007-08/F/1019/A/recurrence.pdf.
[5] G. Walter, Computational aspects of three-term Recurrence relations. SIAM review Vol. 9, No. 1, 1967, pp. 24-82.
[6] P. B. Valentin, The Recurrence Relations in Teaching Students of Informatics. Informatics in Education, Vol. 9, No. 2, 2010, 159–170.
[7] H. R. Kenneth, Discrete Mathematics with Applications, McGraw Hill, Sixth Edition, 2007, pp. 475-482.
[8] L. Yuh-Dauh, Recurrence Relations (Difference Equations). National Taiwan University, 2012, pp 504-555.
[9] Y. Henry, A new kind of Solution, and an Application to Recurrence Relations, 2011, pp. 1-6.
[10] N. Balakrishnan, and M. Ahsanullah, Relations for Single and Product moments of record values from Lomax distribution. The Indian Journal of Statistics, 1994, Volume 66, Series B, pp. 140-146.
[11] G. Ajay, and Don Nelson, Summations and Recurrence Relations1 CS331 and CS531 Design and Analysis of Algorithms, 2003, pp. 1-19.
[12] A. L. Miguel, Recurrence Relations, 2003, pp.1-5.
[13] J. Anderson, Discrete Mathematics with Combinatorics. Prentice-Hall, New Jersey, 2001.
[14] S. W. Herbert, Generating functionology, Academic press. Inc. 1994, pp. 1-231.
[15] C. Marcelle, An Econometric characterization of business cycle dynamics with factor structure and regime switching. International Economic Review. 1998, Vol. 39, No. 2, 969-96.
[16] Alexei Krouglov, Simplified Mathematical model of financial crisis. https://mpra.ub.uni-muenchen.de/44021/MPRA Paper No. 44021, posted 27. January 2013 20:35 UTC.
[17] Yi Wen and Jing Wu, Withstanding Great Recession like China. Working Paper 2014-007A http://research.stlouisfed.org/wp/2014/2014-007.pdf.
[18] I. Anderson, A First Course in Discrete Mathematics. Springer-Verlag, London, 2001.
[19] Zhen Huo, Jose-Victor Rios-Rull. Frictions, Asset Price and the Great Recession, 2015, pp. 1-8
[20] Gilchrist Simon, Raphael Schoenle, Jae W. Sim, and Egon Zakrajsek. Inflation Dynamics during the Financial Crisis. Finance Economics Discussion Series 2015-012. Washington: Board of Governors of the Federl Reserve System, http://dx.doi.org/10.17016/FEDS.2015-012. pp. 1-5
[21] Luigi Paciello, Andrea Pozzi, Nicholas Trachter. Price Dynamics with Customer Markets. February 2016, pp. 1-50.
[22] C. Henry Edwards and E. David Penney Elementary Differential Equations, Sixth Edition, PEARSON Prentice Hall, pp. 1-645. 2008.
[23] S. Yu. Slavyanov. A “differential” derivation of the recurrence relations for the classical orthogonal polynomials. Journal of Computational and Applied Mathematics 49 (1993) 251-254North-Holland. Pp.1-4.
[24] Robbie Beyl and Dennis Merino, Solving Recurrence Relations using Differential Operators, 2006, pp. 1-7.
Cite This Article
  • APA Style

    Philip Ajibola Bankole, Ezekiel Kadejo Ojo, Mary Olukemi Odumosu. (2017). On Recurrence Relations and Application in Predicting Price Dynamics in the Presence of Economic Recession. International Journal of Discrete Mathematics, 2(4), 125-131. https://doi.org/10.11648/j.dmath.20170204.12

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    ACS Style

    Philip Ajibola Bankole; Ezekiel Kadejo Ojo; Mary Olukemi Odumosu. On Recurrence Relations and Application in Predicting Price Dynamics in the Presence of Economic Recession. Int. J. Discrete Math. 2017, 2(4), 125-131. doi: 10.11648/j.dmath.20170204.12

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    AMA Style

    Philip Ajibola Bankole, Ezekiel Kadejo Ojo, Mary Olukemi Odumosu. On Recurrence Relations and Application in Predicting Price Dynamics in the Presence of Economic Recession. Int J Discrete Math. 2017;2(4):125-131. doi: 10.11648/j.dmath.20170204.12

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  • @article{10.11648/j.dmath.20170204.12,
      author = {Philip Ajibola Bankole and Ezekiel Kadejo Ojo and Mary Olukemi Odumosu},
      title = {On Recurrence Relations and Application in Predicting Price Dynamics in the Presence of Economic Recession},
      journal = {International Journal of Discrete Mathematics},
      volume = {2},
      number = {4},
      pages = {125-131},
      doi = {10.11648/j.dmath.20170204.12},
      url = {https://doi.org/10.11648/j.dmath.20170204.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170204.12},
      abstract = {Recurrence relations is one of the fundamental Mathematical tools of computation as most computational tasks rely on recursive techniques at one time or the other. In this paper, we present some important theorems on recurrence relations and give more simplified approach of determining an explicit formula for a given recurrence relation subject to specified boundary values (initial conditions). We recursively apply Recurrence Relation technique to model Economic wealth decay as a result of recession. We show both numerical computation and graphical representation of our simple model and analysis of market price dynamics due to Economic recession.},
     year = {2017}
    }
    

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    T1  - On Recurrence Relations and Application in Predicting Price Dynamics in the Presence of Economic Recession
    AU  - Philip Ajibola Bankole
    AU  - Ezekiel Kadejo Ojo
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    T2  - International Journal of Discrete Mathematics
    JF  - International Journal of Discrete Mathematics
    JO  - International Journal of Discrete Mathematics
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    AB  - Recurrence relations is one of the fundamental Mathematical tools of computation as most computational tasks rely on recursive techniques at one time or the other. In this paper, we present some important theorems on recurrence relations and give more simplified approach of determining an explicit formula for a given recurrence relation subject to specified boundary values (initial conditions). We recursively apply Recurrence Relation technique to model Economic wealth decay as a result of recession. We show both numerical computation and graphical representation of our simple model and analysis of market price dynamics due to Economic recession.
    VL  - 2
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Author Information
  • Department of Mathematics, University of Ibadan, Ibadan, Nigeria

  • Department of Mathematics, Adeniran Ogunsanya College of Education, Otto/Ijanikin, Nigeria

  • Department of Mathematics, Adeniran Ogunsanya College of Education, Otto/Ijanikin, Nigeria

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