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The Economic Plausibility of Strict Local Martingales in Financial Modelling

The context for this article is a continuous financial market consisting of a risk-free savings account and a single non-dividend-paying risky security. We present two concrete models for this market, in which strict local martingales play decisive roles. The first admits an equivalent risk-neutral probability measure under which the discounted price of the risky security is a strict local martingale, while the second model does not even admit an equivalent risk-neutral probability measure, since the putative density process for such a measure is itself a strict local martingale. We highlight a number of apparent anomalies associated with both models that may offend the sensibilities of the classically-educated reader. However, we also demonstrate that these issues are easily resolved if one thinks economically about the models in the right way. In particular, we argue that there is nothing inherently objectionable about either model.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 279.

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Length: 19 pages
Date of creation: 01 Jun 2010
Publication status: Published as: Hulley, H., 2010, "The Economic Plausibility of Strict Local Martingales in Financial Modelling", In: Carl Chiarella and Alexander Novikov (eds) Contemporary Quantitative Finance: Essays in Honour of Eckhard Platen, 53-75.
Handle: RePEc:uts:rpaper:279
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