The Martingale Representation in a Progressive Enlargement of a Filtration with Jumps

• 作 者: 熊德文;
• 机 构: 上海交通大学数学系
• 出 处: 第六届全国金融数学与金融工程学科建设与学术研讨会
• 发表日期: 2013年期

　　In this paper,we assume that the filtion F is generated by a d-dimensional Brownian motion W=(W1,…,Wd)as well as an integer-valued random measure μ(du,dy).The random variable ~τ is the default time and L is the default loss.Let G={Gt;t≥0}be the progressive enlargement of F by(~τ,L),i.e.G is the smallest filtration including F such that ~τ is the G-stopping time and L is F~τ-measurable.Under the density hypothesis,we consider the G-decomposition of a(P,F) martingale and the representation of a(G-martingale,We characterize the conditional density process,which allows us to describe the survival process G e×pIicitIy.Then we give the explicit G-decomposition of a F martingale and for a(p,G)-martingale,which can seen as the extension of Callegaro,Jeanblance and 2argari(2010).