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Local martingales, arbitrage, and viability

Author

Listed:
  • Mark Loewenstein

    (John M. Olin School of Business, Washington University in Saint Louis, Campus Box 1133, One Brookings Drive, St. Louis, MO 63130-4899, USA)

  • Gregory A. Willard

    (Sloan School of Management, Massachusetts Institute of Technology, 50 Memorial Drive, E52-431, Cambridge, MA 02142, USA)

Abstract

We revisit a standard model of security prices as Ito processes, and provide some new economic insights about the role of arbitrage and credit limits within such a model. We show that the standard assumptions of a positive state prices and existence of an equivalent martingale measure exclude prices that are viable models of competitive equilibrium and that are potentially useful for modeling actual financial markets. These models have been dismissed in the past as allowing arbitrage, but in fact an agent who prefers more to less and who has limited access to credit may have an optimum.

Suggested Citation

  • Mark Loewenstein & Gregory A. Willard, 2000. "Local martingales, arbitrage, and viability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 135-161.
    • Handle: RePEc:spr:joecth:v:16:y:2000:i:1:p:135-161
    Note: Received: June 9, 1999; revised version: October 4, 1999
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    More about this item

    Keywords

    Arbitrage; Viability; Wealth constraints; Continuous-time financial markets; Equivalent martingale measures.;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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