IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v45y2015i1p1-30.html
   My bibliography  Save this article

A Constructive Proof of the Existence of Collateral Equilibrium for a Two-Period Exchange Economy Based on a Smooth Interior-Point Path

Author

Listed:
  • Wei Ma

Abstract

In the real economic world, we often suffer from the default risk—the present financial crisis could serve as an evidence. The long established idea for inhibiting the default behavior is to resort to collateral, and this idea has profound effect on the market equilibrium. To study this effect, we make an investigation of the economy wherein default risk is present, assets are collateralized and households are risk-averse. We shall prove that the economy is in possession of an equilibrium. This proof is distinct from the existing one, in two respects: First it shows that equilibrium exists for the Leontief utility function, and second it is constructive. By constructive we mean that, on the basis of this proof, we can (and we shall) develop an algorithm for computing that equilibrium. The algorithm developed is of a path-following type. It starts from an economy which consists of several sub-economies, each with a complete market and a Cobb–Douglas utility function; and it terminates at the equilibrium of the economy under consideration. The algorithm is shown by simulation to be effective. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Wei Ma, 2015. "A Constructive Proof of the Existence of Collateral Equilibrium for a Two-Period Exchange Economy Based on a Smooth Interior-Point Path," Computational Economics, Springer;Society for Computational Economics, vol. 45(1), pages 1-30, January.
    • Handle: RePEc:kap:compec:v:45:y:2015:i:1:p:1-30
    DOI: 10.1007/s10614-013-9404-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10614-013-9404-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10614-013-9404-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Piero Gottardi & Felix Kubler, 2015. "Dynamic Competitive Economies with Complete Markets and Collateral Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 1119-1153.
    2. Pradeep Dubey & John Geanakoplos & Martin Shubik, 2005. "Default and Punishment in General Equilibrium," Econometrica, Econometric Society, vol. 73(1), pages 1-37, January.
    3. Magill, Michael & Quinzii, Martine, 1994. "Infinite Horizon Incomplete Markets," Econometrica, Econometric Society, vol. 62(4), pages 853-880, July.
    4. Aloisio Araujo & Mário Rui Páscoa & Juan Pablo Torres-Martínez, 2002. "Collateral Avoids Ponzi Schemes in Incomplete Markets," Econometrica, Econometric Society, vol. 70(4), pages 1613-1638, July.
    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. Araújo, Aloísio & Kubler, Felix & Schommer, Susan, 2012. "Regulating collateral-requirements when markets are incomplete," Journal of Economic Theory, Elsevier, vol. 147(2), pages 450-476.
    7. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
    8. Joseph E. Stiglitz, 1982. "The Inefficiency of the Stock Market Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 241-261.
    9. Zame, William R, 1993. "Efficiency and the Role of Default When Security Markets Are Incomplete," American Economic Review, American Economic Association, vol. 83(5), pages 1142-1164, December.
    10. Douglas W. Diamond, 1984. "Financial Intermediation and Delegated Monitoring," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(3), pages 393-414.
    11. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
    12. 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.
    13. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
    14. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
    15. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    16. Townsend, Robert M., 1979. "Optimal contracts and competitive markets with costly state verification," Journal of Economic Theory, Elsevier, vol. 21(2), pages 265-293, October.
    17. Sabarwal Tarun, 2003. "Competitive Equilibria With Incomplete Markets and Endogenous Bankruptcy," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-42, January.
    18. Douglas Gale & Martin Hellwig, 1985. "Incentive-Compatible Debt Contracts: The One-Period Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 647-663.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wei Ma, 2017. "A Rejoinder to Notes on a ‘Constructive Proof of the Existence of a Collateral Equilibrium’," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 175-176, January.
    2. Venkatachalam Ragupathy & K. Vela Velupillai, 2016. "Notes on a ‘Constructive Proof of the Existence of a Collateral Equilibrium’," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 179-181, June.

    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. John Geanakoplos & William Zame, 2014. "Collateral equilibrium, I: a basic framework," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 443-492, August.
    2. Jürgen Eichberger & Klaus Rheinberger & Martin Summer, 2014. "Credit risk in general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 407-435, October.
    3. Wei Ma & Chuangyin Dang, 2013. "The Optimal Price of Default," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 145-167, May.
    4. 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.
    5. Iraola, Miguel & Torres-Martínez, Juan Pablo, 2013. "Liquidity Contractions, Incomplete Financial Participation and the Prevalence of Negative Equity Non-recourse Loans," MPRA Paper 46838, University Library of Munich, Germany.
    6. repec:fgv:epgrbe:v:67:n:3:a:3 is not listed on IDEAS
    7. Feijó, Ricardo Luis Chaves, 2013. "The General Equilibrium Framework with Default and Collateral," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 67(3), September.
    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. Brunnermeier, Markus K. & Oehmke, Martin, 2013. "Bubbles, Financial Crises, and Systemic Risk," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1221-1288, Elsevier.
    10. Martins-da-Rocha, V. Filipe & Vailakis, Yiannis, 2012. "Endogenous debt constraints in collateralized economies with default penalties," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 1-13.
    11. Ritzberger, Klaus & Tsomocos, Dimitrios P., 2024. "On bankruptcy in general equilibrium with uncertainty," Journal of Economic Theory, Elsevier, vol. 218(C).
    12. A. Jofré & R. T. Rockafellar & R. J-B. Wets, 2017. "General economic equilibrium with financial markets and retainability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 309-345, January.
    13. Mas-Colell, Andreu & Zame, William R., 1996. "The existence of security market equilibrium with a non-atomic state space," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 63-84.
    14. Claudio Mattalia, 2003. "Existence of solutions and asset pricing bubbles in general equilibrium models," ICER Working Papers - Applied Mathematics Series 02-2003, ICER - International Centre for Economic Research.
    15. Tirelli, Mario, 2008. "Constrained inefficiency in GEI: A geometric argument," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1197-1214, December.
    16. Orrillo, Jaime, 2009. "Making promises in infinite-horizon economies with default and collateral," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3055-3068.
    17. Bottazzi, Jean-Marc & Luque, Jaime & Páscoa, Mário R., 2012. "Securities market theory: Possession, repo and rehypothecation," Journal of Economic Theory, Elsevier, vol. 147(2), pages 477-500.
    18. Orrillo, Jaime, 2001. "Default and exogenous collateral in incomplete markets with a continuum of states," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 151-165, February.
    19. Jean-Marc Bonnisseau & Achis Chéry, 2023. "Continuity of marketable payoffs with re-trading," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 31-53, January.
    20. Phelan, Gregory & Toda, Alexis Akira, 2019. "Securitized markets, international capital flows, and global welfare," Journal of Financial Economics, Elsevier, vol. 131(3), pages 571-592.
    21. Martins-da-Rocha, Victor Filipe & Vailakis, Yiannis, 2010. "Competitive equilibria in infinite-horizon collateralized economies with default penalties," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 703, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).

    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:kap:compec:v:45:y:2015:i:1:p:1-30. 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.