2014/05/18 by Shiqi Song, Song, Shiqi
Decision Sciences · Economics, Econometrics and Finance · #60G07 #60G44 #91G40 #Credit Risk and Financial Regulations #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1405.4474
openalex publication_date 2014/05/18 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
Let \mathbbF⊂ \mathbbG be two filtrations and S be a \mathbbF semimartingale possessing a \mathbbF local martingale deflator. Consider τ a \mathbbG stopping time. We study the problem whether Sτ- or Sτ can have \mathbbG 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 \mathbbG local martingale deflators for Sτ- or for Sτ. Among others, it is proved that \mathbbG local martingale deflators are multiples of \mathbbF local martingale deflators, with a multiplicator coming from the multiplicative decomposition of the Azéma supermartingale of τ. The proofs of the necessary/sufficient conditions require various results to be established about Azéma 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.