Consistent price systems for subfiltrations

Consistent price systems for subfiltrations

Asymmetric or partial information in financial markets may be represented by different filtrations. We consider the case of a larger filtration F – the natural filtration of the “model world” – and a subfiltration $\hat{\mathcal F}$ that represents the information available to an agent in the “real...

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Veröffentlicht in:Probability and statistics 2007-02, Vol.11, p.35-39
Hauptverfasser: Gombani, Andrea, Jaschke, Stefan, Runggaldier, Wolfgang
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Sprache:eng
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91B24
93E11
Arbitrage
Consistent price systems
filtering
numeraire
partial information
Prices
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container_title Probability and statistics
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creator Gombani, Andrea
Jaschke, Stefan
Runggaldier, Wolfgang
description Asymmetric or partial information in financial markets may be represented by different filtrations. We consider the case of a larger filtration F – the natural filtration of the “model world” – and a subfiltration $\hat{\mathcal F}$ that represents the information available to an agent in the “real world”. Given a price system on the larger filtration that is represented by a martingale measure Q and an associated numeraire S, we show that there is a canonical and nontrivial numeraire Ŝ such that the price system generated by (Ŝ,Q,$\hat{\mathcal F}$) is consistent, in a sense to be made precise, with the price system generated by (S,Q,F).
doi_str_mv 10.1051/ps:2007004
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source Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection; NUMDAM
subjects 91B24
93E11
Arbitrage
Consistent price systems
filtering
numeraire
partial information
Prices
title Consistent price systems for subfiltrations
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