Jump to ContentJump to Main Navigation
Show Summary Details
More options …

The B.E. Journal of Theoretical Economics

Editor-in-Chief: Schipper, Burkhard

Ed. by Fong, Yuk-fai / Peeters, Ronald / Puzzello , Daniela / Rivas, Javier / Wenzelburger, Jan

IMPACT FACTOR 2018: 0.173
5-year IMPACT FACTOR: 0.248

CiteScore 2018: 0.24

SCImago Journal Rank (SJR) 2018: 0.163
Source Normalized Impact per Paper (SNIP) 2018: 0.186

Mathematical Citation Quotient (MCQ) 2018: 0.08

See all formats and pricing
More options …

On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy

Ronaldo Carpio
  • Corresponding author
  • School of Banking and Finance, University of International Business and Economics, 913 Boxue Bldg, 10 Huixindongjie, Chaoyang District, Beijing, 100029, China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Meixin Guo
Published Online: 2019-10-01 | DOI: https://doi.org/10.1515/bejte-2018-0144


We introduce a novel method of proving existence of rational expectations equilibria (REE) in multi-dimensional CARA-Gaussian environments. Our approach is to construct a mapping from agents’ initial beliefs (which are characterized by a positive semidefinite matrix), to their updated beliefs, after reaching and observing equilibrium; we then show Brouwer’s fixed point theorem applies. We apply our approach to a finite-market version of Admati (1985), which is a multi-asset noisy REE asset pricing model with dispersed information. We present an algorithm to numerically solve for equilibrium of the finite model, as well as several examples illustrating the difference in equilibrium behavior between the finite and infinite models. Our method can be applied to any multi-dimensional REE model with Gaussian uncertainty and behavior that is linear in agents’ information.

Keywords: asymmetric information; noisy rational expectations; equilibrium existence

JEL Classification: C62; G12


  • Admati, A. 1985. “A Noisy Rational Expectations Equilibrium for Multi-Asset Securities Prices.” Econometrica 53 (3): 629–58.CrossrefGoogle Scholar

  • Berinde, V. Iterative Approximation of Fixed Points. Lecture Notes in MathematicsLecture, Berlin: Springer, 2007. DOI: . Crossref

  • Bernhardt, D., and B. Taub. 2008. “Cross-Asset Speculation in Stock Markets.” Journal of Finance 63 (5): 2385–427.Web of ScienceCrossrefGoogle Scholar

  • Bernstein, D. S. 2009. Matrix Mathematics - Theory, Facts, and Formulas, 2nd ed, Princeton, NJ: Princeton University Press.Google Scholar

  • Bhatia, R. 2007. Positive Definite Matrices, Princeton, NJ: Princeton University Press.Google Scholar

  • Breon-Drish, B. 2015. “On Existence and Uniqueness of Equilibrium in a Class of Noisy Rational Expectations Models.” Review of Economic Studies 82: 868–921.CrossrefWeb of ScienceGoogle Scholar

  • Carpio, R., and M. Guo. 2018. “Specialization in Investor Information and the Diversification Discount.” Working paper.

  • Chabakauri, G., K. Yuan, and K. Zachariadis. 2017. “Multi-Asset Noisy Rational Expectations Equilibrium with Contingent Claims.” Working paper.

  • Coval, J. D. 2003. “International Capital Flows When Investors Have Local Information.” Working Paper 04–026, Harvard Business School.

  • Dai, L. 2018. “Asset Bundling and Information Acquisition of Investors with Different Expertise.” Journal of Economic Theory 175: 447–90.Web of ScienceCrossrefGoogle Scholar

  • Glebkin, S., N. Gondhi, and J. Kuong. 2018. “Funding Constraints and Informational Efficiency.” Working paper, INSEAD.

  • Goldstein, I., and L. Yang. 2017. “Information Disclosure in Financial Markets.” Annual Review of Financial Economics 9: 101–25.CrossrefWeb of ScienceGoogle Scholar

  • Goldstein, I., and L. Yang. 2019. “Good Disclosure, bad Disclosure.” Journal of Financial Economics 131 (1): 118–38.CrossrefWeb of ScienceGoogle Scholar

  • Grossman, S. 1976. “On the Efficiency of Competitive Stock Markets Where Trades Have Diverse Information.” The Journal of finance 31 (2): 573–85.CrossrefGoogle Scholar

  • Grossman, S., and J. Stiglitz. 1980. “On the Impossibility of Informationally Efficient Markets.” American Economic Review 70: 393–408.Google Scholar

  • He, H., and J. Wang. 1995. “Differential Information and Dynamic Behavior of Stock Trading Volume.” Review of Financial Studies 8 (4): 919–72.CrossrefGoogle Scholar

  • Hellwig, M. F. 1980. “On the Aggregation of Information in Competitive Markets.” Journal of Economic Theory 22: 477–98.CrossrefGoogle Scholar

  • Horn, R. A. The Hadamard Product. In: Johnson Charles R., editors. Matrix Theory and Applications (Processdings of Symposia in Applied Mathematics 40) Amer. Math. Soc.: Providence, RI, 1990:87–169.

  • Kyle, A. 1989. “Informed Speculation with Imperfect Competition.” Review of Economic Studies 56: 317–55.CrossrefGoogle Scholar

  • Lou, Youcheng, Sahar Parsa, Debraj Ray, Duan Li, and Shouyang Wang. Information aggregation in a financial market with general signal structure. Journal of Economic Theory 2019(183):594–624. DOI: .CrossrefWeb of Science

  • Liu, Jianzhou 2005. “Eigenvalue and Singular Value Inequalities of Schur Complements,” in The Schur Complement and its Applications, edited by Fuzhen Zhang. Boston, MA: Springer.Google Scholar

  • Mukhopadhyay, N. 2000. Probability and Statistical Inference, Boca Raton, FL: CRC Press.Google Scholar

  • Nezafat, M., M. Schroder, and Q. Wang. 2017. “Short-Sale Constraints, Information Acquisition, and Asset Prices.” Journal of Economic Theory 172: 273–312.CrossrefWeb of ScienceGoogle Scholar

  • Pálvölgyi, D., and G. Venter. 2015a. “Multiple Equilibria in Noisy Rational Expectations Economies.” Working paper.

  • Pálvölgyi, D., and G. Venter. 2015b. “On Equilibrium Uniqueness in Multi-Asset Noisy Rational Expectations Economies.” Working paper.

  • Peress, J. 2005. “Information vs. Entry Costs: What Explains US Stock Market Evolution?” Journal of Financial and Quantitative Analysis 40 (3): 563–94.CrossrefGoogle Scholar

  • Schott, J. R. 2017. Matrix Analysis for Statistics, 3rd. Hoboken, NJ: John Wiley and Sons.Google Scholar

  • Veldkamp, L. 2006. “Information Markets and the Comovement of Asset Prices.” Review of Economic Studies 73: 823–45.CrossrefGoogle Scholar

  • Villalonga, B. 2004. “Diversification Discount or Premium? New Evidence from the Business Information Tracking Series.” The Journal of Finance 59 (2): 479–506.CrossrefGoogle Scholar

  • Watanabe, M. 2008. “Price Volatility and Investor Behavior in an Overlapping Generations Model with Information Asymmetry.” Journal of Finance 63 (1): 229–72.CrossrefWeb of ScienceGoogle Scholar

  • Yu, F. 2008 . “Analyst Coverage and Earnings Management.” Journal of Financial Economics 88: 245– 271.CrossrefWeb of ScienceGoogle Scholar

  • Zhou, C. 1998. “Dynamic Portfolio Choice and Asset Pricing with Differential Information.” Journal of Economic Dynamics and Control 22: 1027–51.CrossrefGoogle Scholar

About the article

Published Online: 2019-10-01

Citation Information: The B.E. Journal of Theoretical Economics, Volume 20, Issue 1, 20180144, ISSN (Online) 1935-1704, DOI: https://doi.org/10.1515/bejte-2018-0144.

Export Citation

© 2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in