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

Listed author(s):
  • Darong Dai

    ()

    (Nanjing University, Nanjing, China)

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    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.

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

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

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    Handle: RePEc:wei:journl:v:3:y:2013:i:2:p:86-110
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    1. Manuel Amador & Iván Werning & George-Marios Angeletos, 2006. "Commitment vs. Flexibility," Econometrica, Econometric Society, vol. 74(2), pages 365-396, 03.
    2. Cvitanic, Jaksa & Wang, Hui, 2001. "On optimal terminal wealth under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 223-231, April.
    3. Kamihigashi, Takashi & Roy, Santanu, 2007. "A nonsmooth, nonconvex model of optimal growth," Journal of Economic Theory, Elsevier, vol. 132(1), pages 435-460, January.
    4. de la Croix, David & Ponthiere, Gregory, 2010. "On the Golden Rule of capital accumulation under endogenous longevity," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 227-238, March.
    5. 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 661-669, October.
    6. 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.
    7. Sahashi, Yoshinao, 2002. "The convergence of optimal forestry control," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 179-214, May.
    8. 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 671-679, October.
    9. 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.
    10. 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.
    11. 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.
    12. Mikhail Anufriev, 2008. "Wealth-driven competition in a speculative financial market: examples with maximizing agents," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 363-380.
    13. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-643, August.
    14. Lawrence Blume & David Easley, 2006. "If You're so Smart, why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Econometrica, Econometric Society, vol. 74(4), pages 929-966, 07.
    15. Nishimura, Kazuo & Shimomura, Koji, 2002. "Trade and Indeterminacy in a Dynamic General Equilibrium Model," Journal of Economic Theory, Elsevier, vol. 105(1), pages 244-260, July.
    16. 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.
    17. 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.
    18. Chakraborty, Shankha, 2004. "Endogenous lifetime and economic growth," Journal of Economic Theory, Elsevier, vol. 116(1), pages 119-137, May.
    19. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, 06.
    20. Markus K. Brunnermeier & Stefan Nagel, 2008. "Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-evidence on Individuals," American Economic Review, American Economic Association, vol. 98(3), pages 713-736, June.
    21. Darong Dai & Kunrong Shen & Ruihua Ma, 2013. "A Case Against Zero Capital-Income Taxation," Frontiers of Economics in China, Higher Education Press, vol. 8(1), pages 64-90, March.
    22. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
    23. De Long, J Bradford, et al, 1991. "The Survival of Noise Traders in Financial Markets," The Journal of Business, University of Chicago Press, vol. 64(1), pages 1-19, January.
    24. Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-620, April.
    25. Lionel W. McKenzie, 2012. "turnpike theory," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
    26. Yano, Makoto, 1984. "The primal route to the turnpike and asymptotic stability," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 225-234, December.
    27. Anufriev, Mikhail & Dindo, Pietro, 2010. "Wealth-driven selection in a financial market with heterogeneous agents," Journal of Economic Behavior & Organization, Elsevier, vol. 73(3), pages 327-358, March.
    28. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    29. Yano, Makoto, 1984. "Competitive Equilibria on Turnpikes in a McKenzie Economy, I: A Neighborhood Turnpike Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(3), pages 695-717, October.
    30. 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.
    31. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
    32. Guerrero-Luchtenberg, C.L., 2000. "A uniform neighborhood turnpike theorem and applications," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 329-357, November.
    33. 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 647-674.
    34. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    35. Stanley R. Pliska, 1986. "A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 371-382, May.
    36. Alexander Schied, 2005. "Optimal Investments for Robust Utility Functionals in Complete Market Models," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 750-764, August.
    37. 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.
    38. Yano, Makoto, 1984. "The turnpike of dynamic general equilibrium paths and its insensitivity to initial conditions," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 235-254, December.
    39. 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.
    40. 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.
    41. Roy Radner, 1961. "Prices and the Turnpike: III. Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem," Review of Economic Studies, Oxford University Press, vol. 28(2), pages 98-104.
    42. 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.
    43. Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, Oxford University Press, vol. 95(2), pages 375-382.
    44. 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.
    45. 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.
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