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Filtration shrinkage, the structure of deflators, and failure of market completeness

Constantinos Kardaras (k.kardaras@lse.ac.uk) and Johannes Ruf (j.ruf@lse.ac.uk)
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Constantinos Kardaras: London School of Economics and Political Science
Johannes Ruf: London School of Economics and Political Science

Finance and Stochastics, 2020, vol. 24, issue 4, No 2, 901 pages

Abstract: Abstract We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale parts in the multiplicative Doob–Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller information market. Via use of a Bayesian filtering approach, we demonstrate the exact mechanism of how updates on the possible class of models under less information result in the strict supermartingale property of projections of such deflators. Finally, we demonstrate that these projections are unable to span all possible local martingale deflators in the smaller information market, by investigating a situation where market completeness is not retained under filtration shrinkage.

Keywords: Bayes rule; Brownian motion; Deflator; Lévy transform; Local martingale; Market completeness; Predictable representation property; 60G44; 60H10; 91G20 (search for similar items in EconPapers)
JEL-codes: C11 G13 G14 (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00780-020-00435-2

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