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Market imperfections, equilibrium and arbitrage

Author

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  • Elyès Jouini

Abstract

The theory of asset pricing, which takes its roots in the Arrow-Debreu model (Theory of value [1959, chap. 7]), the Black and Sholes formula (1973) and Cox and Ross (1976 a and b), has been formalized in a general framework by Harrison and Kreps (1979), Harrison and Pliska (1979) and Kreps (1981). In these models, securities markets are assumed to be frictionless. The main result is that a price process is arbitrage free (or, equivalently, compatible with some equilibrium) if and only if it is, when appropriately renormalized, a martingale for some equivalent probability measure. The theory of pricing by arbitrage follows from there. Contingent claims can be priced by taking their expected value with respect to an equivalent martingale measure. If this value is unique, the claim is said to be priced by arbitrage. The new probabilities can be interpreted as state prices (the prices of $1$ dollar tomorrow in each state of the world) or as the intertemporal marginal rates of substitution of an agent maximizing his expected utility. In this work, we will propose a general model that takes frictions into account.

Suggested Citation

  • Elyès Jouini, 2003. "Market imperfections, equilibrium and arbitrage," Finance 0312005, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0312005
    Note: Type of Document - pdf; prepared on Win98; pages: 55
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    Cited by:

    1. Dokuchaev, N. G. & Savkin, Andrey V., 2004. "Universal strategies for diffusion markets and possibility of asymptotic arbitrage," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 409-419, June.
    2. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    3. Nikolai Dokuchaev, 2002. "Pricing rule based on non-arbitrage arguments for random volatility and volatility smile," Papers math/0205120, arXiv.org.
    4. Jouini, Elyes, 2000. "Price functionals with bid-ask spreads: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 547-558, December.

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    JEL classification:

    • G - Financial Economics

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