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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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    Citations

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    Cited by:

    1. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2015. "Non-Arbitrage Under Additional Information for Thin Semimartingale Models," Papers 1505.00997, arXiv.org.
    2. Bernt {O}ksendal & Agn`es Sulem, 2013. "Dynamic robust duality in utility maximization," Papers 1304.5040, arXiv.org, revised Sep 2015.
    3. Eckhard Platen & Renata Rendek, 2017. "Market Efficiency and the Growth Optimal Portfolio," Research Paper Series 386, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Nuno Azevedo & Diogo Pinheiro & Stylianos Xanthopoulos & Athanasios Yannacopoulos, 2016. "Who would invest only in the risk-free asset?," Papers 1608.02446, arXiv.org.
    5. 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.
    6. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19.
    7. Claudio Fontana, 2013. "Weak and strong no-arbitrage conditions for continuous financial markets," Papers 1302.7192, arXiv.org, revised May 2014.
    8. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2.
    9. Claudio Fontana, 2013. "No-arbitrage conditions and absolutely continuous changes of measure," Papers 1312.4296, arXiv.org, revised Mar 2014.

    More about this item

    Keywords

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

    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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