IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Wealth Martingale and Neighborhood Turnpike Property In Dynamically Complete Market With Heterogeneous Investors

  • Darong Dai

    ()

    (Nanjing University, Nanjing, China)

Registered author(s):

    In the current paper, a dynamically complete financial market with finite and countable heterogeneous investors has been constructed. Self-dynamic game is defined, that is, the investors determine the optimal bankruptcy time first, and then the optimal portfolio policy. Sub-game perfect Nash equilibrium bankruptcy time is derived and it is confirmed that there exists a unique value of efficient terminal wealth for each investor. The interesting theorem of the current paper proves that the vector of efficient terminal wealth exhibits neighborhood turnpike property if the corresponding optimal path of wealth accumulation is a martingale for each investor. This result would be regarded as an interesting neighborhood turnpike theorem in mathematical finance because it focuses on terminal wealth accumulation of the investors which indeed plays a crucial role in mathematical finance. And it also provides us with an internal\intrinsic and a simple relationship between fairness and efficiency characterizaions of the modern financial-market institutions.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.ecrg.ro/files/p2013.3(2)1y2.pdf
    Download Restriction: no

    Article provided by Weissberg Publishing in its journal Economic Research Guardian.

    Volume (Year): 3 (2013)
    Issue (Month): 2 (December)
    Pages: 86-110

    as
    in new window

    Handle: RePEc:wei:journl:v:3:y:2013:i:2:p:86-110
    Contact details of provider:

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. 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.
    2. Robert M. Anderson & Roberto C. Raimondo, 2008. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Econometrica, Econometric Society, vol. 76(4), pages 841-907, 07.
    3. Luo, Guo Ying, 1998. "Market Efficiency and Natural Selection in a Commodity Futures Market," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 647-74.
    4. Guerrero-Luchtenberg, C.L., 2000. "A uniform neighborhood turnpike theorem and applications," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 329-357, November.
    5. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
    6. DE LA CROIX, David & PONTHIÈRE, Grégory, 2008. "On the Golden Rule of capital accumulation under endogenous longevity," CORE Discussion Papers 2008049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Dai, Darong, 2011. "Modeling the minimum time needed to economic maturity," MPRA Paper 40583, University Library of Munich, Germany, revised 08 Aug 2012.
    8. Mikhail Anufriev, 2005. "Wealth-Driven Competition in a Speculative Financial Market: Examples with Maximizing Agents," LEM Papers Series 2005/27, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    9. Makoto Yano, 1999. "Stability and Turnpike Theorems in Dynamic Competitive Equilibrium," The Japanese Economic Review, Japanese Economic Association, vol. 50(4), pages 398-421, December.
    10. McKenzie, Lionel W, 1976. "Turnpike Theory," Econometrica, Econometric Society, vol. 44(5), pages 841-65, September.
    11. Kamihigashi, Takashi & Roy, Santanu, 2007. "A nonsmooth, nonconvex model of optimal growth," Journal of Economic Theory, Elsevier, vol. 132(1), pages 435-460, January.
    12. Liutang Gong & Heng-fu Zou, 2000. "Foreign Aid Reduces Domestic Capital Accumulation and Increases Foreign Borrowing: A Theoretical Analysis," Annals of Economics and Finance, Society for AEF, vol. 1(1), pages 147-163, May.
    13. Koji Shimomura & Kazuo Nishimura, 2001. "Trade and Indeterminacy in a Dynamic General Equilibrium Model," Discussion Paper Series 117, Research Institute for Economics & Business Administration, Kobe University.
    14. Atsumasa Kondo, 2008. "On The Inefficacy Of Temporary Policy In A Dynamic General Equilibrium With Money," The Japanese Economic Review, Japanese Economic Association, vol. 59(3), pages 324-344.
    15. Debraj Ray, 2010. "The Phelps-Koopmans theorem and potential optimality," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 11-28.
    16. Mikhail Anufriev & Pietro Dindo, 2007. "Wealth-driven Selection in a Financial Market with Heterogeneous Agents," LEM Papers Series 2007/27, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    17. Becker, Robert A, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, MIT Press, vol. 95(2), pages 375-82, September.
    18. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2006. "Asset price and wealth dynamics in a financial market with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1755-1786.
    19. Sahashi, Yoshinao, 2002. "The convergence of optimal forestry control," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 179-214, May.
    20. Chakraborty, Shankha, 2004. "Endogenous lifetime and economic growth," Journal of Economic Theory, Elsevier, vol. 116(1), pages 119-137, May.
    21. C. Chiarella & X-Z. He, 2001. "Asset price and wealth dynamics under heterogeneous expectations," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 509-526.
    22. Makoto Yano, 1998. "On the Dual Stability of a von Neumann Facet and the Inefficacy of Temporary Fiscal Policy," Econometrica, Econometric Society, vol. 66(2), pages 427-452, March.
    23. Cvitanic, Jaksa & Wang, Hui, 2001. "On optimal terminal wealth under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 223-231, April.
    24. Coles, Jeffrey Link, 1985. "Equilibrium Turnpike Theory with Constant Returns to Scale and Possible Heterogeneous Discount Factors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 671-79, October.
    25. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, 06.
    26. J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1988. "The Survival of Noise Traders in Financial Markets," NBER Working Papers 2715, National Bureau of Economic Research, Inc.
    27. Ellison, Glenn & Fudenberg, Drew, 1992. "Rules of Thumb for Social Learning," IDEI Working Papers 17, Institut d'Économie Industrielle (IDEI), Toulouse.
    28. Brock, William A. & Scheinkman, JoseA., 1976. "Global asymptotic stability of optimal control systems with applications to the theory of economic growth," Journal of Economic Theory, Elsevier, vol. 12(1), pages 164-190, February.
    29. Lawrence Blume & David Easley, 2001. "If You're So Smart, Why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Working Papers 01-06-031, Santa Fe Institute.
    30. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
    31. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    32. Liutang Gong & Heng-fu Zou, 2003. "Fiscal Federalism, Public Capital Formation, and Endogenous Growth," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 471-490, November.
    33. Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-20, April.
    34. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
    35. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
    36. McKenzie, Lionel W., 1982. "A primal route to the Turnpike and Liapounov stability," Journal of Economic Theory, Elsevier, vol. 27(1), pages 194-209, June.
    37. Yano, Makoto, 1985. "Competitive Equilibria on Turnpikes in a McKenzie Economy, II: An Asymptotic Turnpike Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 661-69, October.
    38. David De La Croix & Grégory Ponthière, 2008. "On the Golden Rule of capital accumulation under endogenous longevity," PSE Working Papers halshs-00586242, HAL.
    39. Tao Pang, 2006. "Stochastic Portfolio Optimization With Log Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 869-887.
    40. Darong Dai, 2012. "Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology," Annals of Economics and Finance, Society for AEF, vol. 13(2), pages 381-423, November.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:wei:journl:v:3:y:2013:i:2:p:86-110. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mihai Mutascu)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.