IDEAS home Printed from https://ideas.repec.org/p/cdl/econwp/qt0zq6v5gd.html
   My bibliography  Save this paper

Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets

Author

Listed:
  • Anderson, Robert M.
  • Raimondo, Roberto C.

Abstract

We prove existence of equilibrium in a continuous-time securities market in which the securities are potentially dynamically complete: the number of securities is at least one more than the number of independent sources of uncertainty. We prove that dynamic completeness of the candidate equilibrium price process follows from mild exogenous assumptions on the economic primitives of the model. Our result is universal, rather than generic: dynamic completeness of the candidate equilibrium price process and existence of equilibrium follow from the way information is revealed in a Brownian filtration, and of a mild exogenous nondegeneracy condition on the terminal security dividends. The nondegeneracy condition, which requires that finding one point at which a determinant of a Jacobian matrix of dividends is nonzero, is very easy to check. We find that the equilibrium prices, consumptions, and trading strategies are well-behaved functions of the stochastic process describing the evolution of information. We prove that equilibria of discrete approximations converge to equilibria of the continuous-time economy.

Suggested Citation

  • Anderson, Robert M. & Raimondo, Roberto C., 2007. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Department of Economics, Working Paper Series qt0zq6v5gd, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  • Handle: RePEc:cdl:econwp:qt0zq6v5gd
    as

    Download full text from publisher

    File URL: https://www.escholarship.org/uc/item/0zq6v5gd.pdf;origin=repeccitec
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
    2. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    3. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 4, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
    4. Basak, Suleyman & Cuoco, Domenico, 1998. "An Equilibrium Model with Restricted Stock Market Participation," The Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 309-341.
    5. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-1297, November.
    6. P. Jean-Jacques Herings & Felix Kubler, 2002. "Computing Equilibria in Finance Economies," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 637-646, November.
    7. Nigel J. Cutland & Ekkehard Kopp & Walter Willinger, 1993. "From Discrete to Continuous Financial Models: New Convergence Results For Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 101-123, April.
    8. Robert Anderson & Roberto Raimondo, 2005. "Market clearing and derivative pricing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(1), pages 21-34, January.
    9. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    10. Nigel Cutland & Ekkehard Kopp & Walter Willinger, 1991. "A Nonstandard Approach to Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 1-38, October.
    11. Hindy, Ayman & Huang, Chi-fu & Kreps, David, 1992. "On intertemporal preferences in continuous time : The case of certainty," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 401-440.
    12. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    13. Robert M. Anderson & Roberto C. Raimondo, 2006. "Equilibrium Pricing of Derivative Securities in Dynamically Incomplete Markets," Studies in Economic Theory, in: Christian Schultz & Karl Vind (ed.), Institutions, Equilibria and Efficiency, chapter 3, pages 27-48, Springer.
    14. Ioannis Karatzas & John P. Lehoczky & Steven E. Shreve, 1990. "Existence and Uniqueness of Multi-Agent Equilibrium in a Stochastic, Dynamic Consumption/Investment Model," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 80-128, February.
    15. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818728, October.
    16. Hindy, Ayman & Huang, Chi-fu, 1993. "Optimal Consumption and Portfolio Rules with Durability and Local Substitution," Econometrica, Econometric Society, vol. 61(1), pages 85-121, January.
    17. Detemple, Jerome B. & Karatzas, Ioannis, 2003. "Non-addictive habits: optimal consumption-portfolio policies," Journal of Economic Theory, Elsevier, vol. 113(2), pages 265-285, December.
    18. Brown, Donald J & Robinson, Abraham, 1975. "Nonstandard Exchange Economies," Econometrica, Econometric Society, vol. 43(1), pages 41-56, January.
    19. Frank Riedel & Peter Bank, 2001. "Existence and structure of stochastic equilibria with intertemporal substitution," Finance and Stochastics, Springer, vol. 5(4), pages 487-509.
    20. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    21. Keisler, H Jerome, 1996. "Getting to a Competitive Equilibrium," Econometrica, Econometric Society, vol. 64(1), pages 29-49, January.
    22. Duffie, Darrell & Shafer, Wayne, 1986. "Equilibrium in incomplete markets: II : Generic existence in stochastic economies," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 199-216, June.
    23. 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.
    24. Riedel, Frank, 2001. "Existence of Arrow-Radner Equilibrium with Endogenously Complete Markets under Incomplete Information," Journal of Economic Theory, Elsevier, vol. 97(1), pages 109-122, March.
    25. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524131, October.
    26. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818735, October.
    27. Mas-Colell, Andreu & Richard, Scott F., 1991. "A new approach to the existence of equilibria in vector lattices," Journal of Economic Theory, Elsevier, vol. 53(1), pages 1-11, February.
    28. Khan, M. Ali & Sun, Yeneng, 2001. "Asymptotic Arbitrage and the APT with or without Measure-Theoretic Structures," Journal of Economic Theory, Elsevier, vol. 101(1), pages 222-251, November.
    29. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524124, October.
    30. 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.
    31. 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.
    32. Lars Nielsen, 2007. "Dividends in the theory of derivative securities pricing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 447-471, June.
    33. Hindy, Ayman & Huang, Chi-fu, 1992. "Intertemporal Preferences for Uncertain Consumption: A Continuous Time Approach," Econometrica, Econometric Society, vol. 60(4), pages 781-801, July.
    34. Dana, Rose Anne, 1993. "Existence and Uniqueness of Equilibria When Preferences Are Additively Separable," Econometrica, Econometric Society, vol. 61(4), pages 953-957, July.
    35. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    36. Nielsen, Lars Tyge, 1999. "Pricing and Hedging of Derivative Securities," OUP Catalogue, Oxford University Press, number 9780198776192.
    37. Magill, Michael J. P. & Shafer, Wayne J., 1990. "Characterisation of generically complete real asset structures," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 167-194.
    38. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
    39. Siu-Ah Ng, 2003. "Hypermodels in Mathematical Finance:Modelling via Infinitesimal Analysis," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4529, August.
    40. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818742, October.
    41. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    42. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
    43. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524117, October.
    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. Theodoros Diasakos, 2008. "Comparative Statics of Asset Prices," Carlo Alberto Notebooks 72, Collegio Carlo Alberto, revised 2011.

    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. 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.
    2. repec:dau:papers:123456789/5374 is not listed on IDEAS
    3. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    4. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
    5. Basak, Suleyman, 1999. "On the fluctuations in consumption and market returns in the presence of labor and human capital: An equilibrium analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 23(7), pages 1029-1064, June.
    6. Chabakauri, Georgy & Han, Brandon Yueyang, 2020. "Collateral constraints and asset prices," Journal of Financial Economics, Elsevier, vol. 138(3), pages 754-776.
    7. Alejandro Jofré & R. Terry Rockafellar & Roger J-B. Wets, 2007. "Variational Inequalities and Economic Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 32-50, February.
    8. Paul Willen & Felix Kubler, 2006. "Collateralized Borrowing And Life-Cycle Portfolio Choice," 2006 Meeting Papers 578, Society for Economic Dynamics.
    9. Frederik Herzberg, 2013. "First steps towards an equilibrium theory for Lévy financial markets," Annals of Finance, Springer, vol. 9(3), pages 543-572, August.
    10. Theodoros M. Diasakos, 2011. "A Simple Characterization of Dynamic Completeness in Continuous Time," Carlo Alberto Notebooks 211, Collegio Carlo Alberto.
    11. Jiang, Wang, 1996. "The term structure of interest rates in a pure exchange economy with heterogeneous investors," Journal of Financial Economics, Elsevier, vol. 41(1), pages 75-110, May.
    12. Liutang Gong & William Smith & Heng-fu Zou, 2007. "Asset Prices and Hyperbolic Discounting," Annals of Economics and Finance, Society for AEF, vol. 8(2), pages 397-414, November.
    13. Peter Koudijs & Hans-Joachim Voth, 2016. "Leverage and Beliefs: Personal Experience and Risk-Taking in Margin Lending," American Economic Review, American Economic Association, vol. 106(11), pages 3367-3400, November.
    14. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach," Operations Research, INFORMS, vol. 49(3), pages 372-397, June.
    15. Bertsimas, Dimitris. & Kogan, Leonid, 1974- & Lo, Andrew W., 1997. "Pricing and hedging derivative securities in incomplete markets : an e-arbitrage approach," Working papers WP 3973-97., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    16. Barbachan, José Fajardo, 2002. "Equilibrium in stochastic economies with incomplete financial markets," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 22(1), May.
    17. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 1997. "Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model," NBER Working Papers 6250, National Bureau of Economic Research, Inc.
    18. Jon Danielsson & Hyun Song Shin & Jean-Pierre Zigrand, 2012. "Endogenous Extreme Events and the Dual Role of Prices," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 111-129, July.
    19. Ehling, Paul & Heyerdahl-Larsen, Christian, 2015. "Complete and incomplete financial markets in multi-good economies," Journal of Economic Theory, Elsevier, vol. 160(C), pages 438-462.
    20. Ana Fostel & John Geanakoplos, 2016. "Financial Innovation, Collateral, and Investment," American Economic Journal: Macroeconomics, American Economic Association, vol. 8(1), pages 242-284, January.
    21. Herzberg, Frederik, 2011. "On the foundations of Lévy finance. Equilibrium for a single-agent financial market with jumps," Center for Mathematical Economics Working Papers 406, Center for Mathematical Economics, Bielefeld University.

    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:cdl:econwp:qt0zq6v5gd. 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: Lisa Schiff (email available below). General contact details of provider: https://edirc.repec.org/data/ibbrkus.html .

    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.