Let F be a filtration on some probability space and let \mathfrak{t be two filtrations and S be a F semimartingale possessing a F local martingale deflator. Consider \tau a G stopping } time. We denote by \mathbb{G or S^{\tau} can have \mathbb{G} local martingale deflators. A suitable theoretical framework is set up in this paper, within which necessary/sufficient conditions for the problem to be solved have been proved. Under these conditions, we will construct \mathbb{G} local martingale deflators for S^{\tau-} or for S^{\tau}. Among others, it is proved that \mathbb{G} local martingale deflators are multiples of \mathbb{F} local martingale deflators, with a multiplicator coming from the multiplicative decomposition of the Az\'ema supermartingale of \tau. The proofs of the necessary/sufficient conditions require various results to be established about Az\'ema supermartingale, about local martingale deflator, about filtration enlargement, which are interesting in themselves. Our study is based on a filtration enlargement setting. For applications, it is important to have a method to infer the existence of such setting from the knowledge of the market information. This question is discussed at the end of the paper} .
Let F \subset \mathbb{G be two filtrations and S be a F semimartingale possessing a F local martingale deflator. Consider \tau a G stopping } time. We study the problem whether S^{\tau- or S^{\tau} can have \mathbb{G} local martingale deflators. A suitable theoretical framework is set up in this paper, within which necessary/sufficient conditions for the problem to be solved have been proved. Under these conditions, we will construct \mathbb{G} local martingale deflators for S^{\tau-} or for S^{\tau}. Among others, it is proved that \mathbb{G} local martingale deflators are multiples of \mathbb{F} local martingale deflators, with a multiplicator coming from the multiplicative decomposition of the Az\'ema supermartingale of \tau. The proofs of the necessary/sufficient conditions require various results to be established about Az\'ema supermartingale, about local martingale deflator, about filtration enlargement, which are interesting in themselves. Our study is based on a filtration enlargement setting. For applications, it is important to have a method to infer the existence of such setting from the knowledge of the market information. This question is discussed at the end of the paper} .
R
be a filtration on some probability space and let \mathfrak{t
\subset \mathbb{G
R
denote by \mathbb{G
study the problem whether S^{\tau-