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Generalized supermartingale deflators under limited information

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  • Constantinos Kardaras

Abstract

We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integrator. We obtain the equivalence of the boundedness in probability of the set of terminal wealth outcomes (which in turn is equivalent to the weak market viability condition of absence of arbitrage of the first kind) with the existence of at least one strictly positive deflator that makes the deflated wealth processes have a generalized supermartingale property.

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  • Constantinos Kardaras, 2009. "Generalized supermartingale deflators under limited information," Papers 0904.2913, arXiv.org, revised Oct 2010.
    • Handle: RePEc:arx:papers:0904.2913
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    1. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
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