IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1301.4881.html
   My bibliography  Save this paper

On the optimal allocation of assets in investment portfolio with application of modern portfolio and nonlinear dynamic chaos theories in investment, commercial and central banks

Author

Listed:
  • Dimitri O. Ledenyov
  • Viktor O. Ledenyov

Abstract

The investment economy is a main characteristic of prosperous society. The investment portfolio management is a main financial problem, which has to be solved by the investment, commercial and central banks with the application of modern portfolio theory in the investment economy. We use the learning analytics together with the integrative creative imperative intelligent conceptual co-lateral adaptive thinking with the purpose to advance our scientific knowledge on the diversified investment portfolio management in the nonlinear dynamic financial system. We apply the econophysics principles and the econometrics methods with the aim to find the solution to the problem of the optimal allocation of assets in the investment portfolio, using the advanced risk management techniques with the efficient frontier modeling in agreement with the modern portfolio theory and using the stability management techniques with the dynamic regimes modeling on the bifurcation diagram in agreement with the dynamic chaos theory. We show that the bifurcation diagram, created with the use of the logistic function in Matlab, can provide some valuable information on the stability of combining risky investments in the investment portfolio, solving the problem of optimization of assets allocation in the investment portfolio. We propose the Ledenyov investment portfolio theorem, based on the Lyapunov stability criteria, with the aim to create the optimized investment portfolio with the uncorrelated diversified assets, which can deliver the increased expected returns to the institutional and private investors in the nonlinear dynamic financial system in the frames of investment economy.

Suggested Citation

  • Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "On the optimal allocation of assets in investment portfolio with application of modern portfolio and nonlinear dynamic chaos theories in investment, commercial and central banks," Papers 1301.4881, arXiv.org, revised Feb 2013.
    • Handle: RePEc:arx:papers:1301.4881
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1301.4881
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2012. "On the Risk Management with Application of Econophysics Analysis in Central Banks and Financial Institutions," Papers 1211.4108, arXiv.org.
    2. John Y. Campbell & Karine Serfaty‐De Medeiros & Luis M. Viceira, 2010. "Global Currency Hedging," Journal of Finance, American Finance Association, vol. 65(1), pages 87-121, February.
    3. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, January.
    4. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    5. Bikas K. Chakrabarti & Anirban Chakraborti, 2010. "Fifteen Years of Econophysics Research," Papers 1010.3401, arXiv.org.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. Viktor O. Ledenyov & Dimitri O. Ledenyov, 2012. "Designing the new architecture of international financial system in era of great changes by globalization," Papers 1206.2778, arXiv.org.
    8. Merton, Robert C, 1998. "Applications of Option-Pricing Theory: Twenty-Five Years Later," American Economic Review, American Economic Association, vol. 88(3), pages 323-349, June.
    9. Hsieh, David A, 1991. "Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
    10. Viktor O. Ledenyov & Dimitri O. Ledenyov, 2012. "Shaping the international financial system in century of globalization," Papers 1206.2022, arXiv.org.
    11. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    12. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    13. Harry Markowitz, 1956. "The optimization of a quadratic function subject to linear constraints," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 111-133, March.
    14. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2012. "On the new central bank strategy toward monetary and financial instabilities management in finances: Econophysical analysis of nonlinear dynamical financial systems," Papers 1211.1897, arXiv.org.
    15. Black, Fischer & Scholes, Myron S, 1972. "The Valuation of Option Contracts and a Test of Market Efficiency," Journal of Finance, American Finance Association, vol. 27(2), pages 399-417, May.
    16. Merton, Robert C. & Bodie, Zvi, 1993. "Deposit insurance reform: a functional approach," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 38(1), pages 1-34, June.
    17. Black, Fischer, 1990. "Equilibrium Exchange Rate Hedging," Journal of Finance, American Finance Association, vol. 45(3), pages 899-907, July.
    18. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    19. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, January.
    20. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    21. Treynor, Jack L & Black, Fischer, 1973. "How to Use Security Analysis to Improve Portfolio Selection," The Journal of Business, University of Chicago Press, vol. 46(1), pages 66-86, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "To the problem of evaluation of market risk of global equity index portfolio in global capital markets," MPRA Paper 47708, University Library of Munich, Germany, revised 20 Jun 2013.
    2. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "Some thoughts on accurate characterization of stock market indexes trends in conditions of nonlinear capital flows during electronic trading at stock exchanges in global capital markets," MPRA Paper 49921, University Library of Munich, Germany.
    3. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    4. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "To the problem of turbulence in quantitative easing transmission channels and transactions network channels at quantitative easing policy implementation by central banks," Papers 1305.5656, arXiv.org, revised May 2013.
    5. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "On the accurate characterization of business cycles in nonlinear dynamic financial and economic systems," Papers 1304.4807, arXiv.org.
    6. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "On the theory of firm in nonlinear dynamic financial and economic systems," Papers 1302.6721, arXiv.org, revised Mar 2013.
    7. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks," MPRA Paper 50235, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2012. "On the Risk Management with Application of Econophysics Analysis in Central Banks and Financial Institutions," Papers 1211.4108, arXiv.org.
    2. David S. Jones & V. Vance Roley, 1981. "Bliss Points in Mean-Variance Portfolio Models," NBER Technical Working Papers 0019, National Bureau of Economic Research, Inc.
    3. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    4. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    5. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    6. Teresa Garcia & Daniel Borrego, 2017. "Markowitz Efficient Frontier And Capital Market Line – Evidence From The Portuguese Stock Market," Portuguese Journal of Management Studies, ISEG, Universidade de Lisboa, vol. 22(1), pages 3-23.
    7. Gregory Phelan & Alexis Akira Toda, 2015. "On the Robustness of Theoretical Asset Pricing Models," Department of Economics Working Papers 2015-10, Department of Economics, Williams College.
    8. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "To the problem of turbulence in quantitative easing transmission channels and transactions network channels at quantitative easing policy implementation by central banks," Papers 1305.5656, arXiv.org, revised May 2013.
    9. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    10. Lin, Wen-chang & Lu, Jin-ray, 2012. "Risky asset allocation and consumption rule in the presence of background risk and insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 150-158.
    11. Benjamin M. Friedman & V. Vance Roley, 1985. "Aspects of Investor Behavior Under Risk," NBER Working Papers 1611, National Bureau of Economic Research, Inc.
    12. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    13. Brisset, Nicolas, 2017. "On Performativity: Option Theory And The Resistance Of Financial Phenomena," Journal of the History of Economic Thought, Cambridge University Press, vol. 39(4), pages 549-569, December.
    14. Dangl, Thomas & Randl, Otto & Zechner, Josef, 2016. "Risk control in asset management: Motives and concepts," CFS Working Paper Series 546, Center for Financial Studies (CFS).
    15. Venegas-Martínez, Francisco & Polanco-Gaytán, Mayrén (ed.), 2011. "Macroeconomía Estocástica," Sección de Estudios de Posgrado e Investigación de la Escuela Superios de Economía del Instituto Politécnico Nacional, Escuela Superior de Economía, Instituto Politécnico Nacional, edition 1, volume 1, number 005, January.
    16. Huang, Hung-Hsi & Wang, Ching-Ping, 2013. "Portfolio selection and portfolio frontier with background risk," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 177-196.
    17. Merton, Robert, 1990. "Capital market theory and the pricing of financial securities," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 1, chapter 11, pages 497-581, Elsevier.
    18. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "On the accurate characterization of business cycles in nonlinear dynamic financial and economic systems," Papers 1304.4807, arXiv.org.
    19. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "On the theory of firm in nonlinear dynamic financial and economic systems," Papers 1302.6721, arXiv.org, revised Mar 2013.
    20. Guiso, Luigi & Sodini, Paolo, 2013. "Household Finance: An Emerging Field," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1397-1532, Elsevier.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1301.4881. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.