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

Kardaras, Constantinos and Ruf, Johannes (2020) Filtration shrinkage, the structure of deflators, and failure of market completeness. Finance and Stochastics, 24 (4). 871 - 901. ISSN 0949-2984

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Identification Number: 10.1007/s00780-020-00435-2

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.

Item Type: Article
Official URL: https://www.springer.com/journal/780
Additional Information: © 2020 The Authors
Divisions: Statistics
Mathematics
Subjects: Q Science > QA Mathematics
H Social Sciences > HG Finance
JEL classification: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C11 - Bayesian Analysis
G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
G - Financial Economics > G1 - General Financial Markets > G14 - Information and Market Efficiency; Event Studies
Date Deposited: 03 Jun 2020 08:51
Last Modified: 20 Jul 2021 02:56
URI: http://eprints.lse.ac.uk/id/eprint/104695

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