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Discrete versus continuous time models: Local martingales and singular processes in asset pricing theory

  • Jarrow, Robert
  • Protter, Philip

In economic theory, both discrete and continuous time models are commonly believed to be equivalent in the sense that one can always be used to approximate the other, or equivalently, any phenomena present in one is also present in the other. This common belief is misguided. Both (strict) local martingales and singular processes exist in continuous time, but not in discrete time models. More importantly, their existence reflects real economic phenomena related to arbitrage opportunities, large traders, asset price bubbles, and market efficiency. And as an approximation to trading opportunities in real markets, continuous trading provides a better fit and should be the preferred modeling approach for asset pricing theory.

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Article provided by Elsevier in its journal Finance Research Letters.

Volume (Year): 9 (2012)
Issue (Month): 2 ()
Pages: 58-62

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Handle: RePEc:eee:finlet:v:9:y:2012:i:2:p:58-62
Contact details of provider: Web page: http://www.elsevier.com/locate/frl

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  1. Pal, Soumik & Protter, Philip, 2010. "Analysis of continuous strict local martingales via h-transforms," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1424-1443, August.
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  9. Soumik Pal & Philip Protter, 2007. "Analysis of continuous strict local martingales via h-transforms," Papers 0711.1136, arXiv.org, revised Jun 2010.
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