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

Autor:	Kardaras, Constantinos, Ruf, Johannes
Rok vydání:	2019
Předmět:	Mathematics - Probability Quantitative Finance - Mathematical Finance
Druh dokumentu:	Working Paper
Popis:	We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part 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. Comment: Minor corrections; Accepted for publication by Finance and Stochastics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1912.04652 Zobrazit plný text záznamu View this record from Arxiv