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Local martingales, arbitrage, and viability

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  • 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)

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    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.

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    Bibliographic Info

    Article provided by Springer in its journal Economic Theory.

    Volume (Year): 16 (2000)
    Issue (Month): 1 ()
    Pages: 135-161

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    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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    Web page: http://link.springer.de/link/service/journals/00199/index.htm

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    Related research

    Keywords: Arbitrage; Viability; Wealth constraints; Continuous-time financial markets; Equivalent martingale measures.;

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    Cited by:
    1. Claudio Fontana, 2013. "No-arbitrage conditions and absolutely continuous changes of measure," Papers 1312.4296, arXiv.org, revised Mar 2014.
    2. Claudio Fontana & Bernt {\O}ksendal & Agn\`es Sulem, 2013. "Market viability and martingale measures under partial information," Papers 1302.4254, arXiv.org, revised Oct 2013.
    3. Bernt \Oksendal & Agn\`es Sulem, 2013. "A stochastic control approach to robust duality in utility maximization," Papers 1304.5040, arXiv.org, revised Dec 2013.
    4. Claudio Fontana, 2013. "Weak and strong no-arbitrage conditions for continuous financial markets," Papers 1302.7192, arXiv.org, revised May 2014.

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