Integral representations of martingales for progressive enlargements of filtrations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Aksamit, Anna¹  Jeanblanc, Monique²  Rutkowski, Marek^1,3 

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

[2] Univ Paris Saclay, Univ Evry Val dEssonne, UMR CNRS 8071, Lab Math & Modelisat dEvry LaMME, 23 Blvd France, F-91037 Evry, France

[3] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00661 Warsaw, Poland

关键词: Predictable representation property;    Poisson process;    Random time;    Progressive enlargement;    Pseudo-stopping time;   

DOI  :  10.1016/j.spa.2018.04.009

来源: Elsevier

【 摘 要 】

We work in the setting of the progressive enlargement G of a reference filtration F through the observation of a random time tau. We study an integral representation property for some classes of G-martingales stopped at tau. In the first part, we focus on the case where F is a Poisson filtration and we establish a predictable representation property with respect to three G-martingales. In the second part, we relax the assumption that F is a Poisson filtration and we assume that tau is an IF-pseudo-stopping time. We establish integral representations with respect to some G-martingales built from F-martingales and, under additional hypotheses, we obtain a predictable representation property with respect to two G-martingales. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free