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Infinite Horizon Incomplete Markets With A Continuum Of States

Author

Listed:
  • Aloisio Araujo
  • Paulo K. Monteiro
  • M´rio Rui P´ascoa

Abstract

In this paper we address existence of equilibria in an incomplete markets economy with countably many periods and a continuum of states at each node of the infinite tree. We consider two models: one where agents have to honor their commitments and another where default is allowed. In both models, marginal utility of income, at each node, is shown to be bounded, and we prove existence by taking finite‐dimensional approximations and applying Fatou's lemma sequentially.

Suggested Citation

  • Aloisio Araujo & Paulo K. Monteiro & M´rio Rui P´ascoa, 1996. "Infinite Horizon Incomplete Markets With A Continuum Of States," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 119-132, April.
    • Handle: RePEc:bla:mathfi:v:6:y:1996:i:2:p:119-132
    DOI: 10.1111/j.1467-9965.1996.tb00074.x
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    References listed on IDEAS

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    1. A.Araujo & P.K.Monteiro & M.Pascoa, 1994. "Existence of equilibria with infinitely many goods,incomplete markets and bankruptcy," GE, Growth, Math methods 9406001, University Library of Munich, Germany, revised 13 Jun 1994.
    2. Pradeep Dubey & John Geanakoplos & Martin Shubik, 1988. "Default and Efficiency in a General Equilibrium Model with Incomplete Markets," Cowles Foundation Discussion Papers 879R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1989.
    3. Florenzano, Monique & Gourdel, Pascal, 1993. "Incomplete markets in infinite horizon : debt constraints versus node prices," CEPREMAP Working Papers (Couverture Orange) 9329, CEPREMAP.
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    Citations

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    Cited by:

    1. Jean-Marc Bonnisseau & Cuong Le Van & Cuong Tran Viet, 2025. "Incomplete Markets with a Countable Number of States: Equilibrium and No-Arbitrage," Annals of Economics and Statistics, GENES, issue 159, pages 35-78.
    2. Araujo, A. & Fajardo, J & Páscoa, M. R., 2003. "Endogenous Collateral: Arbitrage and Equilibrium without Bounded Short Sales," Finance Lab Working Papers flwp_52, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    3. Felipe Martins-da-Rocha & Yiannis Vailakis, 2008. "Collateral, default penalties and almost finite-time solvency," Levine's Working Paper Archive 122247000000002049, David K. Levine.
    4. Florenzano, Monique & Gourdel, Pascal & Pascoa, Mario Rui, 2001. "Overlapping generations models with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 36(3), pages 201-218, December.
    5. 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.
    6. Hervé Crès & Tobias Markeprand & Mich Tvede, 2016. "Incomplete financial markets and jumps in asset prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 201-219, June.
    7. Monteiro, Paulo Klinger & Pascoa, Mario R., 2000. "Discreteness of equilibria in incomplete markets with a continuum of states," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 229-237, March.
    8. Páscoa, Mário Rui & Seghir, Abdelkrim, 2009. "Harsh default penalties lead to Ponzi schemes," Games and Economic Behavior, Elsevier, vol. 65(1), pages 270-286, January.
    9. 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.
    10. Nicolas Houy & Frédéric Jouneau & François Le Grand, 2020. "Defaulting firms and systemic risks in financial networks: a normative approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 503-526, September.
    11. Aloisio Araujo, 2002. "As Leis de Falência: uma Abordagem Econômica," Working Papers Series 57, Central Bank of Brazil, Research Department.
    12. Pascoa, Mario Rui & Araújo, Aloísio Pessoa de & Barbachan, José Santiago Fajardo, 2001. "Endogenous collateral: arbitrage and equilibrium without bounded short sales," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 418, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    13. Rubén Poblete-Cazenave & Juan Torres-Martínez, 2013. "Equilibrium with limited-recourse collateralized loans," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 181-211, May.
    14. Abdelkrim Seghir, 2006. "An overlapping generations model with non-ordered preferences and numeraire-incomplete markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 28(2), pages 95-112, February.
    15. Maldonado, Wilfredo L. & Orrillo, Jaime, 2006. "Two-Sided Altruism in an OLG Model with Incomplete Markets and Default," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 26(2), November.
    16. Damian Pierri, 2025. "Simulations for models with heterogeneous agents, incomplete markets, real assets and aggregate uncertainty," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 20(1), pages 197-236, January.
    17. Kyle F. Herkenhoff, 2012. "Informal unemployment insurance and labor market dynamics," Working Papers 2012-057, Federal Reserve Bank of St. Louis.
    18. Braido, Luis H.B., 2008. "Trading constraints penalizing default: A recursive approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 157-166, January.

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