IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v18y2001i1p127-157.html
   My bibliography  Save this article

Asymptotic methods for asset market equilibrium analysis

Author

Listed:
  • Sy-Ming Guu

    (Department of Industrial Engineering, Yuan-Ze University, Nei-Li, Taoyuan, Taiwan 32026, R.O.C.)

  • Kenneth L. Judd

    (Hoover Institution, Stanford, CA 94305, USA)

Abstract

General equilibrium analysis is difficult when asset markets are incomplete. We make the simplifying assumption that uncertainty is small and use bifurcation methods to compute Taylor series approximations for asset demand and asset market equilibrium. A computer must be used to derive these approximations since they involve large amounts of algebraic manipulation. We use this method to analyze the allocative and welfare effects of introducing a new security. We find that adding any nontrivial derivative security will raise the price of the risky security relative to the bond when risks are small.

Suggested Citation

  • Sy-Ming Guu & Kenneth L. Judd, 2001. "Asymptotic methods for asset market equilibrium analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 127-157.
    • Handle: RePEc:spr:joecth:v:18:y:2001:i:1:p:127-157
    Note: Received: April 1, 2000; revised version: January 10, 2001
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00199/papers/1018001/10180127.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chiappori, Pierre-Andre & Geoffard, Pierre-Yves & Guesnerie, Roger, 1992. "Sunspot Fluctuations around a Steady State: The Case of Multidimensional, One-Step Forward Looking Economic Models," Econometrica, Econometric Society, vol. 60(5), pages 1097-1126, September.
    2. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, vol. 60(2), pages 471-500, August.
    3. Demarzo, Peter M. & Eaves, B. Curtis, 1996. "Computing equilibria of GEI by relocalization on a Grassmann manifold," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 479-497.
    4. Elul Ronel, 1995. "Welfare Effects of Financial Innovation in Incomplete Markets Economies with Several Consumption Goods," Journal of Economic Theory, Elsevier, vol. 65(1), pages 43-78, February.
    5. Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January.
    6. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 537-542.
    7. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    8. David Cass & Alessandro Citanna, 1998. "Pareto improving financial innovation in incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 467-494.
    9. Schmedders, Karl, 1998. "Computing equilibria in the general equilibrium model with incomplete asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1375-1401, August.
    10. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    11. Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543, December.
    12. Ronald W. Jones, 2018. "The Structure of Simple General Equilibrium Models," World Scientific Book Chapters, in: International Trade Theory and Competitive Models Features, Values, and Criticisms, chapter 4, pages 61-84, World Scientific Publishing Co. Pte. Ltd..
    13. Karl Schmedders, 2001. "Monopolistic security design in finance economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 37-72.
    14. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    15. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 45-75, January.
    16. Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
    17. Tesar, Linda L., 1995. "Evaluating the gains from international risksharing," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 42(1), pages 95-143, June.
    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. Esteban-Bravo, Mercedes, 2004. "An interior point algorithm for computing equilibria in economies with incomplete asset markets," DEE - Working Papers. Business Economics. WB wb046023, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    2. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    3. Hara, Chiaki, 2011. "Pareto improvement and agenda control of sequential financial innovations," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 336-345.
    4. Dorofeenko, Victor & Lee, Gabriel S. & Salyer, Kevin D., 2010. "A new algorithm for solving dynamic stochastic macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 388-403, March.
    5. Zhan, Yang & Dang, Chuangyin, 2021. "Determination of general equilibrium with incomplete markets and default penalties," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 49-59.
    6. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.
    7. Ma, Wei, 2015. "A simple method for computing equilibria when asset markets are incomplete," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 32-38.
    8. P. Jean-Jacques Herings & Felix Kubler, 2002. "Computing Equilibria in Finance Economies," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 637-646, November.
    9. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585, Elsevier.
    10. Sergio Turner, 2004. "Pareto Improving Taxation in Incomplete Markets," Econometric Society 2004 Latin American Meetings 310, Econometric Society.
    11. Schmedders, Karl, 1998. "Computing equilibria in the general equilibrium model with incomplete asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1375-1401, August.
    12. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    13. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    14. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    15. Benigno, Pierpaolo & Woodford, Michael, 2012. "Linear-quadratic approximation of optimal policy problems," Journal of Economic Theory, Elsevier, vol. 147(1), pages 1-42.
    16. Sergio Turner & Norovsambuu Tumennasan, 2006. "Pareto Improving Monetary Policy in Incomplete Markets," Working Papers 2006-04, Brown University, Department of Economics.
    17. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    18. Sergio Turner, 2004. "Pareto Improving Taxation in Incomplete Markets," Econometric Society 2004 North American Summer Meetings 614, Econometric Society.
    19. P. Herings & Karl Schmedders, 2006. "Computing equilibria in finance economies with incomplete markets and transaction costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(3), pages 493-512, April.
    20. Momi, Takeshi, 2009. "Excess demand functions when new assets are introduced," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1832-1843, July.

    More about this item

    Keywords

    General equilibrium; Incomplete asset markets; Perturbation methods; Bifurcation methods.;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:spr:joecth:v:18:y:2001:i:1:p:127-157. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.