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Valuation bubbles and sequential bubbles

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  • Kevin X.D. Huang
  • Jan Werner

Abstract

Price bubbles in an Arrow-Debreu valuation equilibrium in infinite-time economy are a manifestation of lack of countable additivity of valuation of assets. In contrast, known examples of price bubbles in sequential equilibrium in infinite time cannot be attributed to the lack of countable additivity of valuation. In this paper we develop a theory of valuation of assets in sequential markets (with no uncertainty) and study the nature of price bubbles in light of this theory. We consider an operator, called payoff pricing functional, that maps a sequence of payoffs to the minimum cost of an asset holding strategy that generates it. We show that the payoff pricing functional is linear and countably additive on the set of positive payoffs if and only if there is no Ponzi scheme, and provided that there is no restriction on long positions in the assets. In the known examples of equilibrium price bubbles in sequential markets valuation is linear and countably additive. The presence of a price bubble indicates that the asset's dividends can be purchased in sequential markers at a cost lower than the asset's price. We also present examples of equilibrium price bubbles in which valuation is nonlinear but not countably additive.

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Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 303.

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Date of creation: Jun 1997
Date of revision: Dec 1997
Handle: RePEc:upf:upfgen:303

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Web page: http://www.econ.upf.edu/

Related research

Keywords: Asset price bubbles; linear valuation; sequential equilibria; valuation equilibria;

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References

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  1. Kandori, Michihiro, 1988. "Equivalent Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 401-17, August.
  2. Gilles, Christian & LeRoy, Stephen F, 1992. "Bubbles and Charges," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 323-39, May.
  3. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-81, September.
  4. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  5. Werner, Jan, 1997. "Arbitrage, Bubbles, and Valuation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 453-64, May.
  6. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-67, November.
  7. Magill, M. & Quinzii, M., 1993. "Icomplete Markets Over an Infinite Horizon: Long-Lived Securities and Speculative Bubbles," Papers 9321, Southern California - Department of Economics.
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Cited by:
  1. Montrucchio, Luigi & Privileggi, Fabio, 1999. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," POLIS Working Papers 5, Institute of Public Policy and Public Choice - POLIS.
  2. Bhattacharya, Utpal, 2003. "The optimal design of Ponzi schemes in finite economies," Journal of Financial Intermediation, Elsevier, vol. 12(1), pages 2-24, January.

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