Skip to main content
Log in

Discrete-time stochastic equilibrium with infinite horizon incomplete asset markets

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

This paper examines the existence of general equilibrium in a discrete time economy with the infinite horizon incomplete markets. There is a single good at each node in the event tree. The existence of general equilibrium for the infinite horizon economy is proved by taking limit of equilibria in truncated economies in which trade stops at a sequence of dates.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Arrow, K. J., Debreu, G., Existence of an equilibrium for a competitive economy, Econometrica, 1954, 22:265–290.

    Article  MATH  Google Scholar 

  2. Debreu, G., Existence of competitive equilibrium, In: Arrow, K., Intriligator, M., eds., Handbook of Mathematical Economics, Volume 2, 1982.

  3. Mas-Colell, A. & Zame, W. R., Equilibrium theory in infinite dimensional spaces, In: Hildenbrand, W., Sonnenschein, H., eds., Handbook of Mathematical Economics, Volume 4, 1991.

  4. Duffie, D., Shafer, W., Equilibrium in incomplete markets: I.A basic model of generic existence, Journal of Mathematical Economics, 1989, 14:285–300.

    Article  Google Scholar 

  5. Husseini, S. Y., Lasry, J-M, Magill, M. J. P., Existence of equilibrium with incomplete asset markets, Journal of Mathematical Economics, 1990, 19:39–67.

    Article  Google Scholar 

  6. Geanakoplos, G., Shafer, W., Solving systems of simultaneous equations in economics, Journal of Mathematical Economics, 1990, 19:69–93.

    Article  Google Scholar 

  7. Hirsch, M. D., Magill, M. J. P., Mas-Colell, A., A geometric approach to a class of equilibrium existence theorems, Journal of Mathematical Economics, 1990, 19:95–106.

    Article  Google Scholar 

  8. Duffie, D., Shafer, W., Equilibrium in incomplete markets: II. Generic existence in stochastic economies, Journal of Mathematical Economics 1986, 15:199–216.

    Article  MATH  Google Scholar 

  9. Werner, J., Equilibrium of economies with incomplete financial markets, Journal of Economic Theory, 1985, 36:110–119.

    Article  MATH  Google Scholar 

  10. Duffie, D., Stochastic equilibria with incomplete financial markets, Journal of Economic Theory, 1987, 41:405–416.

    Article  MATH  Google Scholar 

  11. Duffie, D., Corrigendum, Journal of Economic Theory, 1989, 49:384.

    Article  Google Scholar 

  12. Levine, D. K., Infinite horizon equilibrium with incomplete markets, Journal of Mathematical Economics, 1989, 18:357–376.

    Article  MATH  Google Scholar 

  13. Levine, D. K., Zame, W. R., Debt constraints and equilibrium in infinite horizon economies with incomplete markets, Journal of Mathematical Economics, 1997, 26:103–131.

    Article  Google Scholar 

  14. Zame, W. R., Efficiency and the role of default when security markets are incomplete, The American Economic Review, 1991, 83:1142–1164.

    Google Scholar 

  15. Zame, W. R., Asymptotic behavior of asset markets: asymptotic inefficiency, In: Becker, R., et al., eds. General Equilibrium, Growth and Trade II, Academic Press, New York, 1993.

    Google Scholar 

  16. Hernandez, A. D., Santos, M. S., Incomplete financial markets with an infinite horizon, In: Becker, R., et al., eds., General Equilibrium, Growth and Trade II, Academic Press, New York, 1993.

    Google Scholar 

  17. Magill, M., Quinzii, M., Infinite horizon incomplete markets, Econometrica 1994, 62:853–880.

    Article  MATH  Google Scholar 

  18. Magill, M., Quinzii, M., Incomplete markets over an infinite horizon: long-lived securities and speculative bubbles, Journal of Mathematical Economics, 1997, 26:133–170.

    Article  Google Scholar 

  19. Duffie, D., Security Markets: Stochastic Models, Stanford University, Academic Press, California, 1988.

    MATH  Google Scholar 

  20. Hildenbrand, W., Core and Equilibria of a Large Economy, Princeton University Press, Princeton, N. J., 1974.

    MATH  Google Scholar 

  21. Magill, M., Shafer, W., Characterization of generically complete real asset structures, Journal of Mathematical Economics, 1990, 19:167–194.

    Article  Google Scholar 

  22. Magill, M., Shafer, W., Incomplete Markets, In: Hildenbrand, W., Sonnenschein, H., eds., Handbook of Mathematical Economics, Volume 4, 1991.

  23. Debreu, G., Theory of Value, Yale University Press, New York, 1959.

    MATH  Google Scholar 

  24. Alipranties, C. D., Brown, D. J. & Burkinshaw, O., Existence and Optimality of Competitive Equilibria, Springer-Verlag, Berlin, Heidelberg, 1989.

    Google Scholar 

  25. Geanakoplos, J., An introduction to general equilibrium with incomplete asset markets, Journal of Mathematical Economics, 1990, 19:1–38.

    Article  Google Scholar 

  26. Werner, J., Structure of financial markets and real indeterminacy of equilibria, Journal of Methematical Economics, 1990, 19:217–232.

    Article  Google Scholar 

  27. Zhang, S. M., Wang, Y. Y., Finite horizon arbitrage-free security markets, Acta Mathematica Scientia, 1998. 18(2), 203–211.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported by a project of Financial Mathematics, Financial Engineering and Financial Management, which is one of “Ninth Five-Year Plan” Major Projects of National Natural Science Foundation of China (79790130), Asset pricing theory with frictional security markets, which is a project of National Natural Science Foundation of China (70003002) and 985 Basic Foundation, School of Economics and Management, Tsinghua University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shunming, Z. Discrete-time stochastic equilibrium with infinite horizon incomplete asset markets. Appl. Math. Chin. Univ. 16, 203–218 (2001). https://doi.org/10.1007/s11766-001-0028-9

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-001-0028-9

Subject Classification

Keywords

Navigation