Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2013), Article ID 268427, 11 pages.

Existence of an Equilibrium for Lower Semicontinuous Information Acquisition Functions

Agnès Bialecki, Eléonore Haguet, and Gabriel Turinici

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Abstract

We consider a two-period model in which a continuum of agents trade in a context of costly information acquisition and systematic heterogeneous expectations biases. Because of systematic biases agents are supposed not to learn from others' decisions. In a previous work under somehow strong technical assumptions a market equilibrium was proved to exist and the supply and demand functions were proved to be strictly monotonic with respect to the price. Here we extend these results under very weak technical assumptions. We also prove that the equilibrium price maximizes the trading volume and further additional properties (such as the antimonotonicity of the trading volume with respect to the marginal information price).

Article information

Source
J. Appl. Math., Volume 2014, Special Issue (2013), Article ID 268427, 11 pages.

Dates
First available in Project Euclid: 1 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1412177635

Digital Object Identifier
doi:10.1155/2014/268427

Mathematical Reviews number (MathSciNet)
MR3200839

Citation

Bialecki, Agnès; Haguet, Eléonore; Turinici, Gabriel. Existence of an Equilibrium for Lower Semicontinuous Information Acquisition Functions. J. Appl. Math. 2014, Special Issue (2013), Article ID 268427, 11 pages. doi:10.1155/2014/268427. https://projecteuclid.org/euclid.jam/1412177635


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References

  • J. M. Keynes, The General Theory of Employment, Interest and Money, Macmillan, London, UK, 1936.
  • H. M. Wu and W. C. Guo, “Speculative trading with rational beliefs and endogenous uncertainty,” Economic Theory, vol. 21, no. 2-3, pp. 263–292, 2003.
  • H. M. Wu and W. C. Guo, “Asset price volatility and trading volume with rational beliefs,” Economic Theory, vol. 23, no. 4, pp. 795–829, 2004.
  • J. A. Scheinkman and W. Xiong, “Heterogeneous beliefs, speculation and trading in financial markets,” in Paris-Princeton Lectures on Mathematical Finance 2003, R. A. Carmona, E. Cinlar, I. Ekeland, E. Jouini, J. A. Scheinkman, and N. Touzi, Eds., vol. 1847 of Lecture Notes in Mathematics, pp. 217–250, Springer, Berlin, Germany, 2004.
  • H. R. Varian, “Divergence of opinion in complete markets: a note,” The Journal of Finance, vol. 40, no. 1, pp. 309–317, 1985.
  • M. Harris and A. Raviv, “Differences of opinion make a horse race,” The Review of Financial Studies, vol. 6, no. 3, pp. 473–506, 1993.
  • S. Morris, “Speculative investor behavior and learning,” Quarterly Journal of Economics, vol. 111, no. 4, pp. 1111–1133, 1996.
  • M. Pagano, “Endogenous market thinness and stock price volatility,” The Review of Economic Studies, vol. 56, no. 2, pp. 269–287, 1989.
  • S. J. Grossman and J. E. Stiglitz, “On the impossibility of informationally efficient markets,” The American Economic Review, vol. 70, no. 3, pp. 393–408, 1980.
  • J. B. de Long, A. Shleifer, L. H. Summers, and R. J. Waldmann, “Noise trader risk in financial markets,” Journal of Political Economy, vol. 98, no. 4, pp. 703–738, 1990.
  • J. Wang, “A model of competitive stock trading volume,” Journal of Political Economy, vol. 102, no. 1, pp. 127–168, 1994.
  • R. E. Verrecchia, “Information acquisition in a noisy rational expectations economy,” Econometrica, vol. 50, no. 6, pp. 1415–1430, 1982.
  • M. O. Jackson, “Equilibrium, price formation, and the value of private information,” The Review of Financial Studies, vol. 4, no. 1, pp. 1–16, 1991.
  • L. Veldkamp, “Media frenzies in markets for financial information,” The American Economic Review, vol. 96, no. 3, pp. 577–601, 2006.
  • K. J. Ko and Z. (James) Huang, “Arrogance can be a virtue: overconfidence, information acquisition, and market efficiency,” Journal of Financial Economics, vol. 84, no. 2, pp. 529–560, 2007.
  • T. Krebs, “Rational expectations equilibrium and the strategic choice of costly information,” Journal of Mathematical Economics, vol. 43, no. 5, pp. 532–548, 2007.
  • J. Litvinova and H. O. Yang, “Endogenous information acquisition: a revisit of the Grossman-Stiglitz model,” Working Paper, Duke University, 2003.
  • L. Peng, “Learning with information capacity constraints,” Journal of Financial and Quantitative Analysis, vol. 40, no. 2, pp. 307–329, 2005.
  • M. Shen and G. Turinici, “Liquidity generated by heterogeneous beliefs and costly estimations,” Networks and Heterogeneous Media, vol. 7, no. 2, pp. 349–361, 2012.
  • R. S. Bucy and P. D. Joseph, Filtering for Stochastic Processes with Applications to Guidance, Interscience Tracts in Pure and Applied Mathematics, Interscience, New York, NY, USA, 1968.
  • J. S. Abarbanell, W. N. Lanen, and R. E. Verrecchia, “Analysts' forecasts as proxies for investor beliefs in empirical research,” Journal of Accounting and Economics, vol. 20, no. 1, pp. 31–60, 1995.
  • L. Peng and W. Xiong, “Time to digest and volatility dynamics,” Working Paper, Baruch College and Princeton University, 2003.
  • K. J. Arrow, Aspects of the Theory of Risk-Bearing. Yrjö Jahnsson lectures, Yrjö Jahnssonin Säätiö, Helsinki, Finland, 1965.
  • S. J. Grossman, “The existence of futures markets, noisy rational expectations and informational externalities,” The Review of Economic Studies, vol. 44, no. 3, pp. 431–449, 1977.
  • S. Grossman, “Further results on the informational efficiency of competitive stock markets,” Journal of Economic Theory, vol. 18, no. 1, pp. 81–101, 1978.
  • S. Grossman, “On the efficiency of competitive stock markets where trades have diverse information,” The Journal of Finance, vol. 31, no. 2, pp. 573–585, 1976.
  • R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, USA, 1970. \endinput