IDEAS home Printed from https://ideas.repec.org/p/man/sespap/1816.html
   My bibliography  Save this paper

Von Neumann-Gale Dynamics, Market Frictions, and Capital Growth

Author

Listed:
  • E. Babaei
  • I.V. Evstigneev
  • K.R. Schenk-Hoppé
  • M.V. Zhitlukhin

Abstract

The aim of this work is to extend the classical capital growth theory pertaining to frictionless financial markets to models taking into account various kinds of frictions, including transaction costs and portfolio constraints. A natural generalization of the notion of a benchmark investment strategy (Platen, Heath and others) is proposed, and it is shown how such strategies can be used for the analysis of growth-optimal investments. The analysis is based on the classical von Neumann-Gale model of economic growth, a stochastic version of which is used in this study as a framework for the modeling of financial markets with frictions.

Suggested Citation

  • E. Babaei & I.V. Evstigneev & K.R. Schenk-Hoppé & M.V. Zhitlukhin, 2018. "Von Neumann-Gale Dynamics, Market Frictions, and Capital Growth," Economics Discussion Paper Series 1816, Economics, The University of Manchester.
    • Handle: RePEc:man:sespap:1816
    as

    Download full text from publisher

    File URL: http://hummedia.manchester.ac.uk/schools/soss/economics/discussionpapers/EDP-1816.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    2. Henry Allen Latane, 1959. "Criteria for Choice Among Risky Ventures," Journal of Political Economy, University of Chicago Press, vol. 67, pages 144-144.
    3. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    4. L. C. MacLean & W. T. Ziemba & G. Blazenko, 1992. "Growth Versus Security in Dynamic Investment Analysis," Management Science, INFORMS, vol. 38(11), pages 1562-1585, November.
    5. Pham, Huyen & Touzi, Nizar, 1999. "The fundamental theorem of asset pricing with cone constraints," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 265-279, March.
    6. Marianne Akian & Agnès Sulem & Michael I. Taksar, 2001. "Dynamic Optimization of Long‐Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 153-188, April.
    7. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    8. Garud Iyengar, 2005. "Universal Investment In Markets With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 359-371, April.
    9. William T. Ziemba & Raymond G. Vickson, 2011. "Models of Optimal Capital Accumulation and Portfolio Selection and the Capital Growth Criterion," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 32, pages 473-485, World Scientific Publishing Co. Pte. Ltd..
    10. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    11. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    12. SCHMEIDLER, David, 1970. "Fatou's lemma in several dimensions," LIDAM Reprints CORE 46, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. McKenzie, Lionel W, 1998. "Turnpikes," American Economic Review, American Economic Association, vol. 88(2), pages 1-14, May.
    14. Evstigneev, Igor V. & Schenk-Hoppe, Klaus Reiner, 2007. "Pure and randomized equilibria in the stochastic von Neumann-Gale model," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 871-887, September.
    15. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    16. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    17. Radner, Roy, 1973. "Optimal stationary consumption with stochastic production and resources," Journal of Economic Theory, Elsevier, vol. 6(1), pages 68-90, February.
    18. repec:dau:papers:123456789/5630 is not listed on IDEAS
    19. Leonard Maclean & William Ziemba & Yuming Li, 2005. "Time to wealth goals in capital accumulation," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 343-355.
    20. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    21. MacLean, Leonard C. & Sanegre, Rafael & Zhao, Yonggan & Ziemba, William T., 2004. "Capital growth with security," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 937-954, February.
    22. J. v. Neumann, 1945. "A Model of General Economic Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 13(1), pages 1-9.
    23. M. Dempster & I. Evstigneev & M. Taksar, 2006. "Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model," Annals of Finance, Springer, vol. 2(4), pages 327-355, October.
    24. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    25. Wael Bahsoun & Igor V. Evstigneev & Michael I. Taksar, 2013. "Growth-optimal investments and numeraire portfolios under transaction costs," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 38, pages 789-808, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    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. E. Babaei & I.V. Evstigneev & K.R. Schenk-Hoppé & M.V. Zhitlukhin, 2018. "Von Neumann-Gale Dynamics and Capital Growth in Financial Markets with Frictions," Economics Discussion Paper Series 1815, Economics, The University of Manchester.
    2. Wael Bahsoun & Igor Evstigneev & Michael Taksar, 2007. "Capital growth theory and von Neumann-Gale dynamics," Economics Discussion Paper Series 0720, Economics, The University of Manchester.
    3. Wael Bahsoun & Igor V. Evstigneev & Michael I. Taksar, 2009. "Growth-optimal investments and numeraire portfolios under transaction costs: An analysis based on the von Neumann-Gale model," Papers 0909.4730, arXiv.org.
    4. Jörn Sass & Manfred Schäl, 2014. "Numeraire portfolios and utility-based price systems under proportional transaction costs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 195-234, October.
    5. Palma, Nuno, 2018. "Money and modernization in early modern England," Financial History Review, Cambridge University Press, vol. 25(3), pages 231-261, December.
    6. Jan Kallsen & Johannes Muhle-Karbe, 2011. "Existence of shadow prices in finite probability spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 251-262, April.
    7. Roux, Alet, 2011. "The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 159-163, March.
    8. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the existence of shadow prices," Working Papers hal-00645980, HAL.
    9. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the Existence of Shadow Prices," Papers 1111.6633, arXiv.org, revised Jan 2013.
    10. E. Babaei & I.V. Evstigneev & K.R. Schenk-Hoppé, 2019. "Log-Optimal and Rapid Paths in von Neumann-Gale Dynamical Systems," Economics Discussion Paper Series 1902, Economics, The University of Manchester.
    11. Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
    12. Lepinette, Emmanuel & Tran, Tuan, 2017. "Arbitrage theory for non convex financial market models," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3331-3353.
    13. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2013. "On the existence of shadow prices," Finance and Stochastics, Springer, vol. 17(4), pages 801-818, October.
    14. Yiqing Lin & Junjian Yang, 2016. "Utility maximization problem with random endowment and transaction costs: when wealth may become negative," Papers 1604.08224, arXiv.org, revised Sep 2016.
    15. Martin Brown & Tomasz Zastawniak, 2020. "Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs," Annals of Finance, Springer, vol. 16(3), pages 423-433, September.
    16. Fontana, Claudio & Runggaldier, Wolfgang J., 2021. "Arbitrage concepts under trading restrictions in discrete-time financial markets," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 66-80.
    17. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    18. Scholz, Peter, 2012. "Size matters! How position sizing determines risk and return of technical timing strategies," CPQF Working Paper Series 31, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    19. Matteo Burzoni, 2015. "Arbitrage and Hedging in model-independent markets with frictions," Papers 1512.01488, arXiv.org, revised Aug 2016.
    20. Jan Kallsen & Johannes Muhle-Karbe, 2009. "Existence of Shadow Prices in Finite Probability Spaces," Papers 0911.4801, arXiv.org, revised Nov 2010.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:man:sespap:1816. 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: Marianne Sensier (email available below). General contact details of provider: https://edirc.repec.org/data/semanuk.html .

    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.